Automated univariate time-series forecasting

Aim

To build an automated system that will fit time-series dataset into different Statistical and Machine Learning Models for multi-step forecasting and return result from the most accurate model.

The rationale for such a system is that it can be used by anyone (with or without STEM background) to easily apply time-series forecasting on their data. Since the models have basic setting, one can get the recommended model for their dataset through this system, then customize/fine-tune the said model to maximize its efficiency.

Models available

ARIMA

ARIMA (Auto Regressive Integrated Moving Average)` model is a generalization of an autoregressive moving average (ARMA) model. Both of these models are fitted to time series data either to better understand the data or to predict future points in the series (forecasting). ARIMA models are applied in some cases where data show evidence of non-stationarity in the sense of mean (but not variance/autocovariance), where an initial differencing step (corresponding to the "integrated" part of the model) can be applied one or more times to eliminate the non-stationarity of the mean function (i.e., the trend).

Prophet

Prophet is a procedure for forecasting time series data based on an additive model where non-linear trends are fit with yearly, weekly, and daily seasonality, plus holiday effects. It works best with time series that have strong seasonal effects and several seasons of historical data. Prophet is robust to missing data and shifts in the trend, and typically handles outliers well. Prophet is open source software released by Facebook’s Core Data Science team.

HWES

HWES (Holt Winter’s Exponential Smoothing), also known as the Triple Exponential Smoothing method, models the next time step as an exponentially weighted linear function of observations at prior time steps, taking trends and seasonality into account. Triple exponential smoothing applies exponential smoothing three times, which is commonly used when there are three high frequency signals to be removed from a time series under study. There are different types of seasonality: 'multiplicative' and 'additive' in nature, much like addition and multiplication are basic operations in mathematics. The method calculates a trend line for the data as well as seasonal indices that weight the values in the trend line based on where that time point falls in the cycle.

forecast_recommender

class forecast_recommender.auto_forecast(evaluate_metric)

Parameters

• evaluate_metric : int

The evaluation metric for learning model (Integer 1 to 8)

Evaluation metric for learning model

1. Mean absolute error (MAE)
2. Mean squared error (MSE)
3. Root Mean Square Error (RMSE)
4. Mean absolute percentage error (MAPE)
5. Symmetric mean absolute percentage error (SMAPE)
6. Mean Forecast Error (MFE)
7. Normalized mean squared error (NMSE)
8. Theil's U statistic

Demo

Demonstration done in forecasting-demo.ipynb

from forecast_recommender import forecast_recommender
import pandas as pd

df1 = pd.read_csv("monthly-car-sales.csv")
recommender = forecast_recommender(df1)
result, model_name = recommender.auto_forecast(1)

==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
ma.L1         -0.8372      0.066    -12.691      0.000      -0.967      -0.708
ma.S.L12      -0.4687      0.114     -4.108      0.000      -0.692      -0.245
sigma2      2.673e+06    4.8e+05      5.573      0.000    1.73e+06    3.61e+06
==============================================================================

==============================================
Metrics for ARIMA Model:
Mean Absolute Error: 1451.103
Mean Squared Error: 18608.652
Root Mean Squared Error: 1711.321
Mean absolute percentage error: 7.871
Scaled Mean absolute percentage error: 8.138
Mean forecast error: 17939.99
Normalised mean squared error: 0.192
Theil's U statistic: 0.0
==============================================


==============================================
Metrics for FBProphet Model:
Mean Absolute Error: 1336.814
Mean Squared Error: 18608.652
Root Mean Squared Error: 1749.191
Mean absolute percentage error: 7.187
Scaled Mean absolute percentage error: 7.407
Mean forecast error: 18094.991
Normalised mean squared error: 0.2
Theil_u_statistic: 0.0
==============================================


==============================================
Metrics for HWES Model:
Mean Absolute Error: 1589.052
Mean Squared Error: 18608.652
Root Mean Squared Error: 2197.325
Mean absolute percentage error: 8.622
Scaled Mean absolute percentage error: 9.334
Mean forecast error: 17159.808
Normalised mean squared error: 0.316
Theil_u_statistic: 0.0
==============================================

print("Best model for this dataset is ", model_name)
print(result)

Best model for this dataset is  FbProphet
           ds          yhat
0  1969-01-01  15396.026630
1  1969-02-01  16165.838547
2  1969-03-01  21369.121163
3  1969-04-01  23494.793981
4  1969-05-01  25004.900023
5  1969-06-01  22263.278413
6  1969-07-01  17926.533617
7  1969-08-01  15754.482263
8  1969-09-01  14262.071702
9  1969-10-01  18697.917520
10 1969-11-01  18592.832407
11 1969-12-01  16406.359115