auto_timeseries_hello.ipynb

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  "metadata": {
    "colab": {
      "name": "auto_timeseries_hello.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyM/TAv4xcBF9Ujr+Mio3Utl",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/microprediction/timeseries-notebooks/blob/main/auto_timeseries_hello.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pxPf4jy3Omj_",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7edbc9fe-3152-4799-da5a-56e703c76d47"
      },
      "source": [
        "!pip install --upgrade statsmodels\n",
        "!pip install auto_ts\n",
        "!pip install fbprophet\n",
        "\n",
        "import logging, sys\n",
        "logging.disable(sys.maxsize)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: fbprophet in /usr/local/lib/python3.6/dist-packages (0.7.1)\n",
            "Requirement already satisfied: Cython>=0.22 in /usr/local/lib/python3.6/dist-packages (from fbprophet) (0.29.17)\n",
            "Requirement already satisfied: cmdstanpy==0.9.5 in /usr/local/lib/python3.6/dist-packages (from fbprophet) (0.9.5)\n",
            "Requirement already satisfied: pystan>=2.14 in /usr/local/lib/python3.6/dist-packages (from fbprophet) (2.19.1.1)\n",
            "Requirement already satisfied: numpy>=1.15.4 in /usr/local/lib/python3.6/dist-packages (from fbprophet) (1.19.4)\n",
            "Requirement already satisfied: pandas>=1.0.4 in /usr/local/lib/python3.6/dist-packages (from fbprophet) (1.1.5)\n",
            "Requirement already satisfied: matplotlib>=2.0.0 in /usr/local/lib/python3.6/dist-packages (from fbprophet) (3.2.1)\n",
            "Requirement already satisfied: LunarCalendar>=0.0.9 in /usr/local/lib/python3.6/dist-packages (from fbprophet) (0.0.9)\n",
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            "Requirement already satisfied: holidays>=0.10.2 in /usr/local/lib/python3.6/dist-packages (from fbprophet) (0.10.4)\n",
            "Requirement already satisfied: setuptools-git>=1.2 in /usr/local/lib/python3.6/dist-packages (from fbprophet) (1.2)\n",
            "Requirement already satisfied: python-dateutil>=2.8.0 in /usr/local/lib/python3.6/dist-packages (from fbprophet) (2.8.1)\n",
            "Requirement already satisfied: tqdm>=4.36.1 in /usr/local/lib/python3.6/dist-packages (from fbprophet) (4.41.1)\n",
            "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.6/dist-packages (from pandas>=1.0.4->fbprophet) (2018.9)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib>=2.0.0->fbprophet) (2.4.7)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib>=2.0.0->fbprophet) (0.10.0)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib>=2.0.0->fbprophet) (1.3.1)\n",
            "Requirement already satisfied: ephem>=3.7.5.3 in /usr/local/lib/python3.6/dist-packages (from LunarCalendar>=0.0.9->fbprophet) (3.7.7.1)\n",
            "Requirement already satisfied: pymeeus<=1,>=0.3.6 in /usr/local/lib/python3.6/dist-packages (from convertdate>=2.1.2->fbprophet) (0.3.7)\n",
            "Requirement already satisfied: korean-lunar-calendar in /usr/local/lib/python3.6/dist-packages (from holidays>=0.10.2->fbprophet) (0.2.1)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from holidays>=0.10.2->fbprophet) (1.15.0)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-KgmO47lOr3S"
      },
      "source": [
        "!pip install microprediction"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p2bh6KxE88So"
      },
      "source": [
        "### Hello world univariate\n",
        "See https://www.microprediction.com/blog/popular-timeseries-packages for more packages"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DUhhIeHhOutZ"
      },
      "source": [
        "from microprediction import MicroReader\n",
        "mr = MicroReader()\n",
        "YS = mr.get_lagged_values(name='emojitracker-twitter-face_with_medical_mask.json')[:125]"
      ],
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ODDpGjVDPDwS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b7063a63-38ed-4bd9-f551-0bc18d68410b"
      },
      "source": [
        "from auto_ts import auto_timeseries\n",
        "import pandas as pd \n",
        "import datetime \n",
        "\n",
        "def predict_one(ys:[float])->float:\n",
        "   \"\"\" Predict the next point in a series \"\"\"\n",
        "   ATS = auto_timeseries(score_type='rmse', forecast_period=1,\n",
        "                time_interval='M',\n",
        "                non_seasonal_pdq=None, seasonality=False, seasonal_period=12,\n",
        "                model_type=['best'],\n",
        "                verbose=0) \n",
        "   df_all = pd.DataFrame(columns=['y'],data=list(ys)+[0])\n",
        "   df_all['ds'] = pd.date_range(start='2021-01-01', periods=len(ys)+1, freq='1M')\n",
        "   df_train = df_all.head(-1)\n",
        "   df_test  = df_all.tail(1)\n",
        "\n",
        "   ATS.fit(df_train,'ds','y')\n",
        "   forecast = ATS.predict(df_test)\n",
        "   print('------')\n",
        "   print(forecast)\n",
        "   print('------')\n",
        "   # Now some absurdity to extract prediction\n",
        "   possible_result_cols = ['mean','yhat']\n",
        "   for col in possible_result_cols:\n",
        "     if col in forecast.columns:\n",
        "       return forecast[col].values[0]   \n",
        "\n",
        "   \n",
        "def predict_all(ys):\n",
        "  \"\"\" The slowest way to do it \"\"\"\n",
        "  burnin = 100\n",
        "  y_hats = list()\n",
        "  for t in range(len(ys)):\n",
        "     if t>burnin:\n",
        "        y_hat = predict_one(ys[:t])\n",
        "     elif t>=1:\n",
        "        y_hat = ys[t-1]\n",
        "     else:\n",
        "        y_hat = 0 \n",
        "     y_hats.append(y_hat)\n",
        "  return y_hats \n",
        "\n",
        "# Try it...\n",
        "XS = predict_all(YS)"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (101, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 3.93\n",
            "    Std Deviation of Originals = 3.24\n",
            "    Normalized RMSE = 121%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 2.40\n",
            "    Std Deviation of Originals = 2.30\n",
            "    Normalized RMSE = 104%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 5.28\n",
            "    Std Deviation of Originals = 4.34\n",
            "    Normalized RMSE = 122%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 3.19\n",
            "    Std Deviation of Originals = 3.96\n",
            "    Normalized RMSE = 81%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 2.98\n",
            "    Std Deviation of Originals = 4.18\n",
            "    Normalized RMSE = 71%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.55739\n",
            "Average CV RMSE of all predictions (micro) = 3.69275\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 12 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.69\n",
            "    Std Deviation of Originals = 3.57\n",
            "    Normalized RMSE = 103%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=766.973, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=612.029, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=701.853, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=594.007, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=585.980, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.26 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.23 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=547.118, Time=0.12 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=546.178, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=545.227, Time=0.04 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=543.270, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=545.215, Time=0.04 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=547.270, Time=0.05 sec\n",
            "\n",
            "Best model:  ARIMA(0,0,0)(0,0,0)[0] intercept\n",
            "Total fit time: 0.935 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 540.8\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 2.78\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 13 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  2.782178\n",
            "0       Prophet  3.557393\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y                mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2029-06-30  10.091712  3.508554       3.215073      16.968351\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (102, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 4.19\n",
            "    Std Deviation of Originals = 2.68\n",
            "    Normalized RMSE = 156%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 3.72\n",
            "    Std Deviation of Originals = 2.59\n",
            "    Normalized RMSE = 144%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 4.09\n",
            "    Std Deviation of Originals = 3.13\n",
            "    Normalized RMSE = 131%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 3.24\n",
            "    Std Deviation of Originals = 3.96\n",
            "    Normalized RMSE = 82%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 2.99\n",
            "    Std Deviation of Originals = 4.18\n",
            "    Normalized RMSE = 71%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.64450\n",
            "Average CV RMSE of all predictions (micro) = 3.67466\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 12 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.67\n",
            "    Std Deviation of Originals = 3.31\n",
            "    Normalized RMSE = 111%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=774.810, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=617.236, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=709.558, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=599.037, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=591.676, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.28 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.25 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=551.546, Time=0.06 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=550.807, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=549.865, Time=0.04 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=547.904, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=549.855, Time=0.03 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=551.904, Time=0.06 sec\n",
            "\n",
            "Best model:  ARIMA(0,0,0)(0,0,0)[0] intercept\n",
            "Total fit time: 0.921 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 545.5\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 2.78\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 14 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  2.778431\n",
            "0       Prophet  3.644502\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y                mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2029-07-31  10.167115  3.496091       3.314903      17.019327\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (103, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 4.19\n",
            "    Std Deviation of Originals = 2.41\n",
            "    Normalized RMSE = 174%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 3.79\n",
            "    Std Deviation of Originals = 3.35\n",
            "    Normalized RMSE = 113%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 4.04\n",
            "    Std Deviation of Originals = 3.83\n",
            "    Normalized RMSE = 105%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 3.30\n",
            "    Std Deviation of Originals = 2.77\n",
            "    Normalized RMSE = 119%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 3.75\n",
            "    Std Deviation of Originals = 4.44\n",
            "    Normalized RMSE = 84%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.81463\n",
            "Average CV RMSE of all predictions (micro) = 3.82678\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 13 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.83\n",
            "    Std Deviation of Originals = 3.43\n",
            "    Normalized RMSE = 111%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=783.351, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=623.012, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=716.688, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=604.725, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=597.463, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.30 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.22 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=557.968, Time=0.07 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=557.203, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=556.173, Time=0.04 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=554.188, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=556.170, Time=0.05 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=558.183, Time=0.06 sec\n",
            "\n",
            "Best model:  ARIMA(0,0,0)(0,0,0)[0] intercept\n",
            "Total fit time: 0.934 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 551.6\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 2.97\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 14 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  2.968932\n",
            "0       Prophet  3.814631\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y                mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2029-08-31  10.357543  3.510396       3.477294      17.237793\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (104, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 3.80\n",
            "    Std Deviation of Originals = 2.24\n",
            "    Normalized RMSE = 170%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 5.06\n",
            "    Std Deviation of Originals = 3.85\n",
            "    Normalized RMSE = 132%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 2.47\n",
            "    Std Deviation of Originals = 3.51\n",
            "    Normalized RMSE = 70%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 4.16\n",
            "    Std Deviation of Originals = 5.22\n",
            "    Normalized RMSE = 80%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 3.22\n",
            "    Std Deviation of Originals = 3.65\n",
            "    Normalized RMSE = 88%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.74108\n",
            "Average CV RMSE of all predictions (micro) = 3.84191\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 12 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.84\n",
            "    Std Deviation of Originals = 3.59\n",
            "    Normalized RMSE = 107%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=790.150, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=630.956, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=722.600, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=612.650, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=605.218, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.30 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.27 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=564.103, Time=0.08 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=563.454, Time=0.04 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=562.575, Time=0.03 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=560.676, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=562.547, Time=0.05 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=557.823, Time=0.30 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=560.077, Time=0.32 sec\n",
            " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=560.083, Time=0.39 sec\n",
            " ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=562.462, Time=0.05 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=562.062, Time=0.40 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0]             : AIC=inf, Time=0.10 sec\n",
            "\n",
            "Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept\n",
            "Total fit time: 2.479 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 557.9\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 3.17\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 15 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  3.167118\n",
            "0       Prophet  3.741076\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y               mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2029-09-30  10.23841  3.548924       3.282648      17.194172\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (105, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 2.71\n",
            "    Std Deviation of Originals = 1.79\n",
            "    Normalized RMSE = 151%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 4.86\n",
            "    Std Deviation of Originals = 3.85\n",
            "    Normalized RMSE = 126%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 2.26\n",
            "    Std Deviation of Originals = 2.17\n",
            "    Normalized RMSE = 104%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 4.17\n",
            "    Std Deviation of Originals = 5.26\n",
            "    Normalized RMSE = 79%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 4.28\n",
            "    Std Deviation of Originals = 4.10\n",
            "    Normalized RMSE = 104%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.65417\n",
            "Average CV RMSE of all predictions (micro) = 3.78715\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 12 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.79\n",
            "    Std Deviation of Originals = 3.70\n",
            "    Normalized RMSE = 102%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=798.689, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=640.569, Time=0.02 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=732.442, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=619.237, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=611.464, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.30 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.22 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=570.732, Time=0.11 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=569.929, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=568.683, Time=0.06 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=566.943, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=568.626, Time=0.04 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=565.130, Time=0.31 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=567.259, Time=0.31 sec\n",
            " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=567.307, Time=0.34 sec\n",
            " ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=569.105, Time=0.05 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=inf, Time=0.44 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0]             : AIC=inf, Time=0.12 sec\n",
            "\n",
            "Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept\n",
            "Total fit time: 2.511 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 558.2\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mProphet\n",
            "    Best Model (Mean CV) Score: 3.65\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 15 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "0       Prophet  3.654173\n",
            "1  auto_SARIMAX  4.410918\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "Building Forecast dataframe. Forecast Period = 1\n",
            "------\n",
            "            ds      trend  ...  multiplicative_terms_upper      yhat\n",
            "105 2029-10-31  10.370385  ...                         0.0  8.670995\n",
            "\n",
            "[1 rows x 16 columns]\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (106, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 2.40\n",
            "    Std Deviation of Originals = 2.30\n",
            "    Normalized RMSE = 104%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 5.28\n",
            "    Std Deviation of Originals = 4.34\n",
            "    Normalized RMSE = 122%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 3.19\n",
            "    Std Deviation of Originals = 3.96\n",
            "    Normalized RMSE = 81%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 2.98\n",
            "    Std Deviation of Originals = 4.18\n",
            "    Normalized RMSE = 71%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 4.53\n",
            "    Std Deviation of Originals = 4.10\n",
            "    Normalized RMSE = 110%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.67784\n",
            "Average CV RMSE of all predictions (micro) = 3.82813\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 13 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.83\n",
            "    Std Deviation of Originals = 3.68\n",
            "    Normalized RMSE = 104%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=806.324, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=645.830, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=738.395, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=624.159, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=616.193, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.28 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.36 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=575.186, Time=0.06 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=574.310, Time=0.06 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=573.131, Time=0.06 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=571.357, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=573.080, Time=0.05 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=570.250, Time=0.27 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=571.789, Time=0.37 sec\n",
            " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=571.848, Time=0.43 sec\n",
            " ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=573.481, Time=0.05 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=inf, Time=0.44 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0]             : AIC=inf, Time=0.27 sec\n",
            "\n",
            "Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept\n",
            "Total fit time: 2.860 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 562.7\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mProphet\n",
            "    Best Model (Mean CV) Score: 3.68\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 16 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "0       Prophet  3.677839\n",
            "1  auto_SARIMAX  4.255353\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "Building Forecast dataframe. Forecast Period = 1\n",
            "------\n",
            "            ds      trend  ...  multiplicative_terms_upper       yhat\n",
            "106 2029-11-30  10.321481  ...                         0.0  10.457258\n",
            "\n",
            "[1 rows x 16 columns]\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (107, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 3.72\n",
            "    Std Deviation of Originals = 2.59\n",
            "    Normalized RMSE = 144%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 4.09\n",
            "    Std Deviation of Originals = 3.13\n",
            "    Normalized RMSE = 131%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 3.24\n",
            "    Std Deviation of Originals = 3.96\n",
            "    Normalized RMSE = 82%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 2.99\n",
            "    Std Deviation of Originals = 4.18\n",
            "    Normalized RMSE = 71%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 4.76\n",
            "    Std Deviation of Originals = 4.56\n",
            "    Normalized RMSE = 104%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.75842\n",
            "Average CV RMSE of all predictions (micro) = 3.81095\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 12 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.81\n",
            "    Std Deviation of Originals = 3.64\n",
            "    Normalized RMSE = 105%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=813.334, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=651.173, Time=0.02 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=744.967, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=630.290, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=621.364, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.31 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.22 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=580.323, Time=0.09 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=579.225, Time=0.04 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=578.264, Time=0.05 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=576.510, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=578.200, Time=0.05 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=574.705, Time=0.30 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=576.418, Time=0.33 sec\n",
            " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=576.464, Time=0.40 sec\n",
            " ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=578.226, Time=0.06 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=578.506, Time=0.48 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0]             : AIC=inf, Time=0.16 sec\n",
            "\n",
            "Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept\n",
            "Total fit time: 2.654 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 567.5\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mProphet\n",
            "    Best Model (Mean CV) Score: 3.76\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 15 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "0       Prophet  3.758416\n",
            "1  auto_SARIMAX  3.959184\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "Building Forecast dataframe. Forecast Period = 1\n",
            "------\n",
            "            ds      trend  ...  multiplicative_terms_upper       yhat\n",
            "107 2029-12-31  10.335722  ...                         0.0  11.001787\n",
            "\n",
            "[1 rows x 16 columns]\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (108, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 3.79\n",
            "    Std Deviation of Originals = 3.35\n",
            "    Normalized RMSE = 113%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 4.04\n",
            "    Std Deviation of Originals = 3.83\n",
            "    Normalized RMSE = 105%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 3.30\n",
            "    Std Deviation of Originals = 2.77\n",
            "    Normalized RMSE = 119%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 3.75\n",
            "    Std Deviation of Originals = 4.44\n",
            "    Normalized RMSE = 84%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 3.97\n",
            "    Std Deviation of Originals = 3.90\n",
            "    Normalized RMSE = 102%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.77107\n",
            "Average CV RMSE of all predictions (micro) = 3.78003\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 13 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.78\n",
            "    Std Deviation of Originals = 3.64\n",
            "    Normalized RMSE = 104%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=820.969, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=657.151, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=751.715, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=635.472, Time=0.02 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=626.093, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.28 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.22 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=584.766, Time=0.08 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=583.609, Time=0.04 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=582.649, Time=0.05 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=580.917, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=582.580, Time=0.04 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=579.335, Time=0.29 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=580.942, Time=0.34 sec\n",
            " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=580.984, Time=0.36 sec\n",
            " ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=582.598, Time=0.05 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=583.109, Time=0.42 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0]             : AIC=inf, Time=0.11 sec\n",
            "\n",
            "Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept\n",
            "Total fit time: 2.431 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 572.3\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 3.15\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 15 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  3.148086\n",
            "0       Prophet  3.771068\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y               mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2030-01-31  9.950471  3.463874       3.161403      16.739539\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (109, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 5.06\n",
            "    Std Deviation of Originals = 3.85\n",
            "    Normalized RMSE = 132%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 2.47\n",
            "    Std Deviation of Originals = 3.51\n",
            "    Normalized RMSE = 70%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 4.16\n",
            "    Std Deviation of Originals = 5.22\n",
            "    Normalized RMSE = 80%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 3.22\n",
            "    Std Deviation of Originals = 3.65\n",
            "    Normalized RMSE = 88%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 3.60\n",
            "    Std Deviation of Originals = 2.86\n",
            "    Normalized RMSE = 126%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.70195\n",
            "Average CV RMSE of all predictions (micro) = 3.80403\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 12 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.80\n",
            "    Std Deviation of Originals = 3.63\n",
            "    Normalized RMSE = 105%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=828.422, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=662.182, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=758.143, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=640.389, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=630.813, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.29 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.27 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=589.092, Time=0.09 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=587.947, Time=0.04 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=586.984, Time=0.05 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=585.256, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=586.915, Time=0.06 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=583.648, Time=0.30 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=585.231, Time=0.35 sec\n",
            " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=585.275, Time=0.36 sec\n",
            " ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=586.929, Time=0.05 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=587.359, Time=0.43 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0]             : AIC=inf, Time=0.18 sec\n",
            "\n",
            "Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept\n",
            "Total fit time: 2.621 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 576.1\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 2.34\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 15 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  2.335459\n",
            "0       Prophet  3.701950\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y               mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2030-02-28  9.813256  3.351652       3.244138      16.382374\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (110, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 4.86\n",
            "    Std Deviation of Originals = 3.85\n",
            "    Normalized RMSE = 126%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 2.26\n",
            "    Std Deviation of Originals = 2.17\n",
            "    Normalized RMSE = 104%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 4.17\n",
            "    Std Deviation of Originals = 5.26\n",
            "    Normalized RMSE = 79%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 4.28\n",
            "    Std Deviation of Originals = 4.10\n",
            "    Normalized RMSE = 104%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 2.02\n",
            "    Std Deviation of Originals = 1.92\n",
            "    Normalized RMSE = 105%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.51678\n",
            "Average CV RMSE of all predictions (micro) = 3.70044\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 12 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.70\n",
            "    Std Deviation of Originals = 3.52\n",
            "    Normalized RMSE = 105%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=836.257, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=667.607, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=765.269, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=645.432, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=636.049, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.26 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.25 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=593.631, Time=0.08 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=592.576, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=591.594, Time=0.06 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=589.870, Time=0.02 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=591.524, Time=0.04 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=588.503, Time=0.31 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=589.965, Time=0.30 sec\n",
            " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=590.025, Time=0.38 sec\n",
            " ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=591.553, Time=0.05 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=592.298, Time=0.42 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0]             : AIC=inf, Time=0.25 sec\n",
            "\n",
            "Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept\n",
            "Total fit time: 2.621 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 581.2\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 1.79\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 15 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  1.787254\n",
            "0       Prophet  3.516778\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y               mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2030-03-31  9.596088  3.484844       2.765919      16.426257\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (111, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 5.28\n",
            "    Std Deviation of Originals = 4.34\n",
            "    Normalized RMSE = 122%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 3.19\n",
            "    Std Deviation of Originals = 3.96\n",
            "    Normalized RMSE = 81%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 2.98\n",
            "    Std Deviation of Originals = 4.18\n",
            "    Normalized RMSE = 71%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 4.53\n",
            "    Std Deviation of Originals = 4.10\n",
            "    Normalized RMSE = 110%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 1.84\n",
            "    Std Deviation of Originals = 1.87\n",
            "    Normalized RMSE = 98%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.56437\n",
            "Average CV RMSE of all predictions (micro) = 3.76476\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 11 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.76\n",
            "    Std Deviation of Originals = 3.52\n",
            "    Normalized RMSE = 107%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=843.709, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=672.640, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=771.532, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=650.230, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=640.754, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.30 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.24 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=597.932, Time=0.08 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=596.886, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=595.913, Time=0.05 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=594.194, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=595.843, Time=0.05 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=592.809, Time=0.28 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=594.241, Time=0.40 sec\n",
            " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=594.305, Time=0.39 sec\n",
            " ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=595.853, Time=0.05 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=596.474, Time=0.57 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0]             : AIC=inf, Time=0.21 sec\n",
            "\n",
            "Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept\n",
            "Total fit time: 2.846 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 585.0\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 1.55\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 15 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  1.546573\n",
            "0       Prophet  3.564369\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y               mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2030-04-30  9.779228  3.298247       3.314781      16.243674\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (112, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 4.09\n",
            "    Std Deviation of Originals = 3.13\n",
            "    Normalized RMSE = 131%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 3.24\n",
            "    Std Deviation of Originals = 3.96\n",
            "    Normalized RMSE = 82%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 2.99\n",
            "    Std Deviation of Originals = 4.18\n",
            "    Normalized RMSE = 71%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 4.76\n",
            "    Std Deviation of Originals = 4.56\n",
            "    Normalized RMSE = 104%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 1.21\n",
            "    Std Deviation of Originals = 1.00\n",
            "    Normalized RMSE = 121%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.25651\n",
            "Average CV RMSE of all predictions (micro) = 3.47155\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 12 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.47\n",
            "    Std Deviation of Originals = 3.33\n",
            "    Normalized RMSE = 104%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=851.544, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=678.051, Time=0.02 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=778.841, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=655.166, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=645.624, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.29 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.23 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=602.568, Time=0.07 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=601.530, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=600.507, Time=0.05 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=598.792, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=600.438, Time=0.05 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=597.619, Time=0.35 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=599.009, Time=0.37 sec\n",
            " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=599.085, Time=0.40 sec\n",
            " ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=600.543, Time=0.05 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=601.258, Time=0.46 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0]             : AIC=inf, Time=0.18 sec\n",
            "\n",
            "Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept\n",
            "Total fit time: 2.697 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 589.6\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 1.64\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 15 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  1.640733\n",
            "0       Prophet  3.256513\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y               mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2030-05-31  9.580013  3.338486         3.0367      16.123325\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (113, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 4.04\n",
            "    Std Deviation of Originals = 3.83\n",
            "    Normalized RMSE = 105%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 3.30\n",
            "    Std Deviation of Originals = 2.77\n",
            "    Normalized RMSE = 119%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 3.75\n",
            "    Std Deviation of Originals = 4.44\n",
            "    Normalized RMSE = 84%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 3.97\n",
            "    Std Deviation of Originals = 3.90\n",
            "    Normalized RMSE = 102%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 1.96\n",
            "    Std Deviation of Originals = 1.67\n",
            "    Normalized RMSE = 117%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.40477\n",
            "Average CV RMSE of all predictions (micro) = 3.48996\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 12 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.49\n",
            "    Std Deviation of Originals = 3.35\n",
            "    Normalized RMSE = 104%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=858.683, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=683.356, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=784.827, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=660.241, Time=0.02 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=650.794, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.31 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.34 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=607.162, Time=0.09 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=606.193, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=605.174, Time=0.05 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=603.494, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=605.096, Time=0.05 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=602.035, Time=0.30 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=603.471, Time=0.43 sec\n",
            " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=603.540, Time=0.39 sec\n",
            " ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=605.158, Time=0.05 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=605.697, Time=0.44 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0]             : AIC=inf, Time=0.20 sec\n",
            "\n",
            "Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept\n",
            "Total fit time: 2.835 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 595.0\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 1.39\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 15 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  1.388770\n",
            "0       Prophet  3.404769\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y                mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2030-06-30  10.140918  3.506542       3.268223      17.013613\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (114, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 2.47\n",
            "    Std Deviation of Originals = 3.51\n",
            "    Normalized RMSE = 70%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 4.16\n",
            "    Std Deviation of Originals = 5.22\n",
            "    Normalized RMSE = 80%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 3.22\n",
            "    Std Deviation of Originals = 3.65\n",
            "    Normalized RMSE = 88%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 3.60\n",
            "    Std Deviation of Originals = 2.86\n",
            "    Normalized RMSE = 126%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 2.17\n",
            "    Std Deviation of Originals = 1.67\n",
            "    Normalized RMSE = 129%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.12246\n",
            "Average CV RMSE of all predictions (micro) = 3.20657\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 12 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.21\n",
            "    Std Deviation of Originals = 3.32\n",
            "    Normalized RMSE = 97%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=866.318, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=688.992, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=792.316, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=665.162, Time=0.02 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=655.594, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.29 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.31 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=611.507, Time=0.07 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=610.551, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=609.518, Time=0.05 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=607.856, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=609.436, Time=0.06 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=606.432, Time=0.29 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=607.872, Time=0.37 sec\n",
            " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=607.945, Time=0.38 sec\n",
            " ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=609.523, Time=0.06 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=610.011, Time=0.48 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0]             : AIC=inf, Time=0.25 sec\n",
            "\n",
            "Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept\n",
            "Total fit time: 2.814 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 604.9\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 1.60\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 15 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  1.600362\n",
            "0       Prophet  3.122460\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y                mean  mean_se  mean_ci_lower  mean_ci_upper\n",
            "2030-07-31  10.275435  3.44782       3.517831      17.033038\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (115, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 2.26\n",
            "    Std Deviation of Originals = 2.17\n",
            "    Normalized RMSE = 104%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 4.17\n",
            "    Std Deviation of Originals = 5.26\n",
            "    Normalized RMSE = 79%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 4.28\n",
            "    Std Deviation of Originals = 4.10\n",
            "    Normalized RMSE = 104%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 2.02\n",
            "    Std Deviation of Originals = 1.92\n",
            "    Normalized RMSE = 105%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 2.64\n",
            "    Std Deviation of Originals = 2.24\n",
            "    Normalized RMSE = 118%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.07316\n",
            "Average CV RMSE of all predictions (micro) = 3.21912\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 12 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.22\n",
            "    Std Deviation of Originals = 3.27\n",
            "    Normalized RMSE = 99%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=874.604, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=694.730, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=799.248, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=671.262, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=661.214, Time=0.04 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.37 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.24 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=617.067, Time=0.07 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=616.001, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=615.096, Time=0.05 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=613.404, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=615.016, Time=0.05 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=612.308, Time=0.39 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=613.625, Time=0.31 sec\n",
            " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=613.706, Time=0.31 sec\n",
            " ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=614.937, Time=0.06 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=inf, Time=0.48 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0]             : AIC=inf, Time=0.25 sec\n",
            "\n",
            "Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept\n",
            "Total fit time: 2.781 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 604.5\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 2.23\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 15 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  2.233234\n",
            "0       Prophet  3.073160\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y               mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2030-08-31  9.573317  3.433841       2.843112      16.303521\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (116, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 3.19\n",
            "    Std Deviation of Originals = 3.96\n",
            "    Normalized RMSE = 81%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 2.98\n",
            "    Std Deviation of Originals = 4.18\n",
            "    Normalized RMSE = 71%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 4.53\n",
            "    Std Deviation of Originals = 4.10\n",
            "    Normalized RMSE = 110%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 1.84\n",
            "    Std Deviation of Originals = 1.87\n",
            "    Normalized RMSE = 98%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 2.69\n",
            "    Std Deviation of Originals = 2.17\n",
            "    Normalized RMSE = 124%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.04654\n",
            "Average CV RMSE of all predictions (micro) = 3.16902\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 11 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.17\n",
            "    Std Deviation of Originals = 3.18\n",
            "    Normalized RMSE = 100%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=882.239, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=699.817, Time=0.02 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=805.765, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=676.063, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=665.875, Time=0.04 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.33 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.22 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=621.419, Time=0.08 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=620.389, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=619.474, Time=0.06 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=617.755, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=619.403, Time=0.06 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=616.816, Time=0.32 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=618.055, Time=0.46 sec\n",
            " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=618.153, Time=0.38 sec\n",
            " ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=619.364, Time=0.06 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=620.384, Time=0.43 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0]             : AIC=inf, Time=0.20 sec\n",
            "\n",
            "Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept\n",
            "Total fit time: 2.814 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 614.7\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 2.41\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 14 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  2.411342\n",
            "0       Prophet  3.046536\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y                mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2030-09-30  10.493636  3.428822       3.773268      17.214004\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (117, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 3.24\n",
            "    Std Deviation of Originals = 3.96\n",
            "    Normalized RMSE = 82%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 2.99\n",
            "    Std Deviation of Originals = 4.18\n",
            "    Normalized RMSE = 71%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 4.76\n",
            "    Std Deviation of Originals = 4.56\n",
            "    Normalized RMSE = 104%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 1.21\n",
            "    Std Deviation of Originals = 1.00\n",
            "    Normalized RMSE = 121%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 3.08\n",
            "    Std Deviation of Originals = 2.30\n",
            "    Normalized RMSE = 134%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.05370\n",
            "Average CV RMSE of all predictions (micro) = 3.25553\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 11 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.26\n",
            "    Std Deviation of Originals = 3.21\n",
            "    Normalized RMSE = 101%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=890.288, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=705.230, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=813.088, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=680.907, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=670.663, Time=0.06 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.29 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.23 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=626.637, Time=0.12 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=625.549, Time=0.06 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=624.451, Time=0.06 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=622.715, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=624.392, Time=0.04 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=622.248, Time=0.31 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=623.524, Time=0.33 sec\n",
            " ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=623.625, Time=0.34 sec\n",
            " ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=624.694, Time=0.06 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=625.746, Time=0.47 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0]             : AIC=inf, Time=0.27 sec\n",
            "\n",
            "Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept\n",
            "Total fit time: 2.738 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 613.9\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 2.72\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 14 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  2.718602\n",
            "0       Prophet  3.053703\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y               mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2030-10-31  9.742038  3.440587       2.998611      16.485465\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (118, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 3.30\n",
            "    Std Deviation of Originals = 2.77\n",
            "    Normalized RMSE = 119%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 3.75\n",
            "    Std Deviation of Originals = 4.44\n",
            "    Normalized RMSE = 84%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 3.97\n",
            "    Std Deviation of Originals = 3.90\n",
            "    Normalized RMSE = 102%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 1.96\n",
            "    Std Deviation of Originals = 1.67\n",
            "    Normalized RMSE = 117%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 3.58\n",
            "    Std Deviation of Originals = 1.52\n",
            "    Normalized RMSE = 236%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.31330\n",
            "Average CV RMSE of all predictions (micro) = 3.38855\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 12 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.39\n",
            "    Std Deviation of Originals = 3.10\n",
            "    Normalized RMSE = 109%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=898.566, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=710.445, Time=0.02 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=820.100, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=686.029, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=675.489, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.30 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.24 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=632.529, Time=0.07 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=631.195, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=630.040, Time=0.06 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=628.224, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=630.001, Time=0.05 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=628.540, Time=0.30 sec\n",
            "\n",
            "Best model:  ARIMA(0,0,0)(0,0,0)[0] intercept\n",
            "Total fit time: 1.239 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 625.2\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 2.35\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 13 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  2.345763\n",
            "0       Prophet  3.313298\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y                mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2030-11-30  10.701885  3.411177       4.016101      17.387669\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (119, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 4.16\n",
            "    Std Deviation of Originals = 5.22\n",
            "    Normalized RMSE = 80%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 3.22\n",
            "    Std Deviation of Originals = 3.65\n",
            "    Normalized RMSE = 88%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 3.60\n",
            "    Std Deviation of Originals = 2.86\n",
            "    Normalized RMSE = 126%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 2.17\n",
            "    Std Deviation of Originals = 1.67\n",
            "    Normalized RMSE = 129%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 3.49\n",
            "    Std Deviation of Originals = 1.52\n",
            "    Normalized RMSE = 230%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.32722\n",
            "Average CV RMSE of all predictions (micro) = 3.39140\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 11 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.39\n",
            "    Std Deviation of Originals = 3.10\n",
            "    Normalized RMSE = 110%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=906.201, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=715.520, Time=0.02 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=826.568, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=690.944, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=680.216, Time=0.06 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.29 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.23 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=636.932, Time=0.11 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=635.584, Time=0.06 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=634.393, Time=0.04 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=632.557, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=634.359, Time=0.04 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=633.149, Time=0.36 sec\n",
            "\n",
            "Best model:  ARIMA(0,0,0)(0,0,0)[0] intercept\n",
            "Total fit time: 1.299 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 629.5\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 2.34\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 13 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  2.339496\n",
            "0       Prophet  3.327218\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y                mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2030-12-31  10.719466  3.396932       4.061602      17.377331\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (120, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 4.17\n",
            "    Std Deviation of Originals = 5.26\n",
            "    Normalized RMSE = 79%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 4.28\n",
            "    Std Deviation of Originals = 4.10\n",
            "    Normalized RMSE = 104%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 2.02\n",
            "    Std Deviation of Originals = 1.92\n",
            "    Normalized RMSE = 105%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 2.64\n",
            "    Std Deviation of Originals = 2.24\n",
            "    Normalized RMSE = 118%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 3.49\n",
            "    Std Deviation of Originals = 2.68\n",
            "    Normalized RMSE = 130%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.31922\n",
            "Average CV RMSE of all predictions (micro) = 3.43193\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 10 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.43\n",
            "    Std Deviation of Originals = 3.21\n",
            "    Normalized RMSE = 107%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=913.217, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=720.839, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=832.652, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=696.896, Time=0.02 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=686.429, Time=0.06 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.39 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.26 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=641.823, Time=0.07 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=640.591, Time=0.06 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=639.574, Time=0.04 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=637.754, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=639.532, Time=0.05 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=637.792, Time=0.29 sec\n",
            "\n",
            "Best model:  ARIMA(0,0,0)(0,0,0)[0] intercept\n",
            "Total fit time: 1.315 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 634.9\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 2.26\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 12 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  2.260000\n",
            "0       Prophet  3.319221\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y                mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2031-01-31  10.601803  3.399075       3.939739      17.263867\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (121, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 2.98\n",
            "    Std Deviation of Originals = 4.18\n",
            "    Normalized RMSE = 71%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 4.53\n",
            "    Std Deviation of Originals = 4.10\n",
            "    Normalized RMSE = 110%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 1.84\n",
            "    Std Deviation of Originals = 1.87\n",
            "    Normalized RMSE = 98%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 2.69\n",
            "    Std Deviation of Originals = 2.17\n",
            "    Normalized RMSE = 124%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 3.40\n",
            "    Std Deviation of Originals = 2.70\n",
            "    Normalized RMSE = 126%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.08851\n",
            "Average CV RMSE of all predictions (micro) = 3.21236\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 11 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.21\n",
            "    Std Deviation of Originals = 2.97\n",
            "    Normalized RMSE = 108%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=921.049, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=727.246, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=840.226, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=702.360, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=691.280, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.28 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.23 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=646.423, Time=0.07 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=645.108, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=644.082, Time=0.06 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=642.302, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=644.032, Time=0.05 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=642.529, Time=0.38 sec\n",
            "\n",
            "Best model:  ARIMA(0,0,0)(0,0,0)[0] intercept\n",
            "Total fit time: 1.263 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 639.3\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 2.45\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 12 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  2.451240\n",
            "0       Prophet  3.088506\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y                mean  mean_se  mean_ci_lower  mean_ci_upper\n",
            "2031-02-28  10.654457  3.38719       4.015686      17.293227\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (122, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 2.99\n",
            "    Std Deviation of Originals = 4.18\n",
            "    Normalized RMSE = 71%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 4.76\n",
            "    Std Deviation of Originals = 4.56\n",
            "    Normalized RMSE = 104%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 1.21\n",
            "    Std Deviation of Originals = 1.00\n",
            "    Normalized RMSE = 121%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 3.08\n",
            "    Std Deviation of Originals = 2.30\n",
            "    Normalized RMSE = 134%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 3.09\n",
            "    Std Deviation of Originals = 3.11\n",
            "    Normalized RMSE = 99%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.02475\n",
            "Average CV RMSE of all predictions (micro) = 3.22728\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 10 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.23\n",
            "    Std Deviation of Originals = 3.08\n",
            "    Normalized RMSE = 105%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=929.573, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=732.991, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=847.365, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=709.004, Time=0.04 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=697.566, Time=0.05 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.27 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.24 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=652.524, Time=0.06 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=651.159, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=650.370, Time=0.04 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=648.531, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=650.328, Time=0.05 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=649.346, Time=0.34 sec\n",
            "\n",
            "Best model:  ARIMA(0,0,0)(0,0,0)[0] intercept\n",
            "Total fit time: 1.214 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 645.2\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 2.83\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 12 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  2.827869\n",
            "0       Prophet  3.024751\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y                mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2031-03-31  10.804557  3.395471       4.149556      17.459559\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (123, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 3.75\n",
            "    Std Deviation of Originals = 4.44\n",
            "    Normalized RMSE = 84%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 3.97\n",
            "    Std Deviation of Originals = 3.90\n",
            "    Normalized RMSE = 102%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 1.96\n",
            "    Std Deviation of Originals = 1.67\n",
            "    Normalized RMSE = 117%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 3.58\n",
            "    Std Deviation of Originals = 1.52\n",
            "    Normalized RMSE = 236%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 3.16\n",
            "    Std Deviation of Originals = 3.11\n",
            "    Normalized RMSE = 101%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.28471\n",
            "Average CV RMSE of all predictions (micro) = 3.36121\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 11 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.36\n",
            "    Std Deviation of Originals = 3.08\n",
            "    Normalized RMSE = 109%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=937.845, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=737.960, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=854.476, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=713.815, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=702.728, Time=0.08 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=667.034, Time=0.26 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.18 sec\n",
            " ARIMA(3,0,2)(0,0,0)[0]             : AIC=inf, Time=0.49 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0]             : AIC=inf, Time=0.23 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0] intercept   : AIC=658.225, Time=0.50 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=656.462, Time=0.31 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=657.995, Time=0.06 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=656.853, Time=0.06 sec\n",
            " ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=659.514, Time=0.39 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=655.931, Time=0.04 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=654.000, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=655.915, Time=0.04 sec\n",
            "\n",
            "Best model:  ARIMA(0,0,0)(0,0,0)[0] intercept\n",
            "Total fit time: 2.761 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 650.4\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mauto_SARIMAX\n",
            "    Best Model (Mean CV) Score: 2.81\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 14 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "1  auto_SARIMAX  2.809756\n",
            "0       Prophet  3.284707\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "------\n",
            "y                mean   mean_se  mean_ci_lower  mean_ci_upper\n",
            "2031-04-30  10.917609  3.393471       4.266529       17.56869\n",
            "------\n",
            "Start of Fit.....\n",
            "    Target variable given as = y\n",
            "Start of loading of data.....\n",
            "Input is data frame. Performing Time Series Analysis\n",
            "ts_column: ds sep: , target: y\n",
            "    Dataframe loaded successfully. Shape of data set = (124, 1)\n",
            "Time Interval is given as M\n",
            "    Correct Time interval given as a valid Pandas date-range frequency...\n",
            "\u001b[1mWARNING: Running best models will take time... Be Patient...\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Prophet Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Facebook Prophet Model...\u001b[0m\n",
            "  Starting Prophet Fit\n",
            "  End of Prophet Fit\n",
            "  Starting Prophet Cross Validation\n",
            "Max. iterations using expanding window cross validation = 5\n",
            "    RMSE = 3.22\n",
            "    Std Deviation of Originals = 3.65\n",
            "    Normalized RMSE = 88%\n",
            "Cross Validation window: 1 completed\n",
            "    RMSE = 3.60\n",
            "    Std Deviation of Originals = 2.86\n",
            "    Normalized RMSE = 126%\n",
            "Cross Validation window: 2 completed\n",
            "    RMSE = 2.17\n",
            "    Std Deviation of Originals = 1.67\n",
            "    Normalized RMSE = 129%\n",
            "Cross Validation window: 3 completed\n",
            "    RMSE = 3.49\n",
            "    Std Deviation of Originals = 1.52\n",
            "    Normalized RMSE = 230%\n",
            "Cross Validation window: 4 completed\n",
            "    RMSE = 3.62\n",
            "    Std Deviation of Originals = 3.81\n",
            "    Normalized RMSE = 95%\n",
            "Cross Validation window: 5 completed\n",
            "Average CV RMSE over 5 windows (macro) = 3.21901\n",
            "Average CV RMSE of all predictions (micro) = 3.26499\n",
            "  End of Prophet Cross Validation\n",
            "Time Taken = 10 seconds\n",
            "---------------------------\n",
            "Final Prophet CV results:\n",
            "---------------------------\n",
            "    RMSE = 3.26\n",
            "    Std Deviation of Originals = 2.73\n",
            "    Normalized RMSE = 120%\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building Auto SARIMAX Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "Running Auto SARIMAX Model...\u001b[0m\n",
            "Performing stepwise search to minimize aic\n",
            " ARIMA(0,0,0)(0,0,0)[0]             : AIC=944.867, Time=0.01 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0]             : AIC=744.290, Time=0.02 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0]             : AIC=860.417, Time=0.03 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0]             : AIC=720.975, Time=0.03 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0]             : AIC=709.648, Time=0.06 sec\n",
            " ARIMA(3,0,1)(0,0,0)[0]             : AIC=inf, Time=0.26 sec\n",
            " ARIMA(2,0,1)(0,0,0)[0]             : AIC=inf, Time=0.23 sec\n",
            " ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=662.911, Time=0.06 sec\n",
            " ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=661.776, Time=0.05 sec\n",
            " ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=661.103, Time=0.04 sec\n",
            " ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=659.229, Time=0.01 sec\n",
            " ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=661.069, Time=0.05 sec\n",
            " ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=660.193, Time=0.48 sec\n",
            "\n",
            "Best model:  ARIMA(0,0,0)(0,0,0)[0] intercept\n",
            "Total fit time: 1.357 seconds\n",
            "\u001b[1mRefitting data with previously found best parameters\u001b[0m\n",
            "    Best aic metric = 655.9\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building VAR Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No VAR model created since no explanatory variables given in data set\u001b[0m\n",
            "\n",
            "\n",
            "==================================================\n",
            "Building ML Model\n",
            "==================================================\n",
            "\n",
            "\n",
            "\u001b[1m\n",
            "No predictors available. Skipping Machine Learning model...\u001b[0m\n",
            "\u001b[1m\n",
            "Best Model is: \u001b[0mProphet\n",
            "    Best Model (Mean CV) Score: 3.22\n",
            "\n",
            "\n",
            "--------------------------------------------------\n",
            "Total time taken: 12 seconds.\n",
            "--------------------------------------------------\n",
            "\n",
            "\n",
            "Leaderboard with best model on top of list:\n",
            "            name      rmse\n",
            "0       Prophet  3.219012\n",
            "1  auto_SARIMAX  3.341935\n",
            "2           VAR       inf\n",
            "3            ML       inf\n",
            "Building Forecast dataframe. Forecast Period = 1\n",
            "------\n",
            "            ds      trend  ...  multiplicative_terms_upper       yhat\n",
            "124 2031-05-31  10.796618  ...                         0.0  11.599657\n",
            "\n",
            "[1 rows x 16 columns]\n",
            "------\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "id": "UsQalSXqS6a4",
        "outputId": "daf3d4aa-672a-4723-ef4b-02f906d83922"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "plt.plot(YS[:25],'*b')\n",
        "plt.plot(XS[:25],'g')"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f7ddd4bcb00>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}