Boosting Time-Series Forecasting Accuracy with SARIMAX Seasonal Interval Automation

Time series analysis and forecasting have been extensively studied in various domains, with researchers proposing numerous techniques and models to capture complex patterns in temporal data. Autoregressive Integrated Moving Average (ARIMA) model has been widely adopted for time series forecasting, capturing the autoregressive (AR), integrated (I), and moving average (MA) components of a time series. To address the limitations of the traditional ARIMA model in handling seasonal patterns, extensions like Seasonal ARIMA (SARIMA) and Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (SARI-MAX) models have been developed. These models incorporate seasonal components and exogenous variables, improving forecasting accuracy by capturing external influences on the time series. This study evaluates the performance of SARIMAX models on two real-world datasets: French Champagne sales from 1964-1972 and Air Passengers data from 1949-1960. For the Champagne dataset, the SARIMAX model with parameters (1, 1, 1) * (1, 1, 0, 6) achieves the lowest AIC of 8.0 and BIC of 18.34. For the Air Passengers dataset, the SARIMAX model with parameters (0, 1, 1) * (1, 1, 1, 12) achieves the lowest AIC of 1020.33 and BIC of 1031.83. Additionally, this study proposes a method for computing seasonality intervals using Double Exponential Smoothing (DES) and statistical techniques to refine the accuracy of seasonal adjustments in SARIMAX model. The results highlight the importance of automating seasonality intervals to improve forecast accuracy across various domains.