Forecasting Multiplicative Seasonality Time-Series with Machine Learning, Time-Series, and Hybrid Models:

Insights from Simulation-based Assessments

Abstract

A prevalent feature of time-series data is multiplicative seasonality, in which the seasonal effects change according to the level of the series. The widely used ARIMA model cannot enhance prediction performance in this situation. By incorporating alternative models into the analysis, researchers can better understand and forecast patterns in time-series data with complex seasonality. Therefore, this study investigates the performance of various forecasting models on time-series data exhibiting multiplicative seasonality. The authors evaluated eleven models, including classical time-series methods like ARIMA and ETS, machine learning models like TBATS, ANN, and several hybrid combinations such as ETS-ARIMA, ETS-TBATS, TBATS-ARIMA TBATS-ETS, TBATS-ANN, STL-ARIMA, STL-ETS. Our analysis utilized both large-scale simulations and real-world datasets to provide a comprehensive assessment. In real-world data applications, the ETS model excelled in forecasting trends with multiplicative seasonality, while SARIMA outperformed other models in datasets with no trend multiplicative seasonality. However, simulation-based analyses revealed more nuanced results. The ETS-ARIMA hybrid model demonstrated superior performance on the UKgas dataset, particularly with simulation sizes of 500 and data sizes of 100, and 200. For the fdeaths dataset, TBATS produced the best results in terms of MSE and RMSE for a simulation size of 500 and data size of 100, whereas the ETS-TBATS model was more effective in terms of MAE and MAPE. Additionally, the TBATS-ARIMA hybrid model consistently outperformed others with data sizes of 200. These findings underscore the importance of selecting customized models based on dataset characteristics to achieve accurate forecasting in time-series data with multiplicative seasonality.