Time Series Forecasting with ARIMA and SARIMA Models

This repository contains Python code for time series forecasting using ARIMA and SARIMA models, focusing on retail sales data analysis. With this project, we will find answers to the following questions:

• Can we predict sales in businesses?
• Which methods allow predicting the future from past data?
• What kind of procedure should be followed in case of missing and erroneous data?
• Are sales affected by seasonality (seasons, months, days of the week, etc.)?
• How do we measure the success of our prediction?

You can visit my medium page for more explanation: (https://medium.com/@asliyalcnn/time-series-forecasting-with-ar%C4%B1ma-and-sar%C4%B1ma-f1a8f4ab5a39)

Overview

Features

• Data Loading and Preprocessing:

  • Loads sales data (data.csv) and store information (store.csv).
  • Adds features like year, month, day, and sales per customer.

• Exploratory Data Analysis:

  • Empirical Cumulative Distribution Function (ECDF) plots for sales, customers, and sale per customer.
  • Weekly sales trends visualization for different stores.

• Data Cleaning:

  • Removes rows with closed stores (Open != 0) and zero sales (Sales != 0).
  • Imputes missing values in CompetitionDistance with the median and other columns with zeros.

• Merging Datasets:

  • Combines sales and store datasets (df_merged) based on store ID.

Analysis

• Stationarity Test:

  • Function test_stationarity checks stationarity using rolling statistics and Augmented Dickey-Fuller (ADF) test.

• Time Series Decomposition:

  • plot_timeseries decomposes sales data into trend and seasonality using seasonal decomposition.

• Autocorrelation and Partial Autocorrelation Analysis:

  • ACF and PACF plots with auto_corr function.

Modeling

• ARIMA and SARIMA Models:

  • Applies models to weekly sales data (df_arima and df_sarima) using auto_arima and statsmodels.

• Model Evaluation:

  • RMSE, MAE, and MAPE for model performance evaluation.

Visualization

• Forecast Visualization:
  • Observed vs. forecasted sales plots using ARIMA and SARIMA models.

Requirements

• Python 3.x
• Required Libraries: pandas, numpy, matplotlib, seaborn, plotly, statsmodels, pmdarima, scikit-learn

• References

• (https://mlpills.dev/time-series/how-to-train-a-sarima-model-step-by-step) access date: 26.12.2023
• (https://people.duke.edu/~rnau/411arim.htm#:~:text=A%20nonseasonal%20ARIMA%20model%20is,errors%20in%20the%20prediction%20equation)
• Wanjuki T.M. & Wagala A. et. al,(2022), “Evaluating the Predictive Ability of Seasonal Autoregressive Integrated Moving Average (SARIMA) Models When Applied to Food and Beverages Price Index in Kenya”, EJ-MATH, European Journal of Mathematics and Statistics, 2736-5484, 29-31
• Wanjuki T.M. & Wagala A. et. al,(2022), “Evaluating the Predictive Ability of Seasonal Autoregressive Integrated Moving Average (SARIMA) Models When Applied to Food and Beverages Price Index in Kenya”, EJ-MATH, European Journal of Mathematics and Statistics, 2736-5484, 29-31
• (https://www.statisticshowto.com/adf-augmented-dickey-fuller-test) access date: 24.12.2023
• (https://www.analyticsvidhya.com/blog/2021/06/statistical-tests-to-check-stationarity-in-time-series-part-1/) access date: 24.12.2023
• (https://permetrics.readthedocs.io/en/latest/pages/regression/RMSE.html) access date: 26.12.2023
• (https://permetrics.readthedocs.io/en/latest/pages/regression/MAE.html) access date: 26.12.2023
• https://docs.oracle.com/en/cloud/saas/planning-budgeting-cloud/pfusu/insights_metrics_MAPE.html#GUID-C33B0F01-83E9-468B-B96C-413A12882334) access date: 26.12.2023

Usage

To run the project:

python time_series_forecasting.py