Enhancing Forecast Accuracy for Damped Trend and Multiplicative Seasonality: A Hybrid Time-Series Framework with Simulation Study

Abstract

Forecasting time series characterized by a damped trend and multiplicative seasonality (DTMS) presents a significant challenge, as conventional models like ARIMA and ETS often fail to capture their complex, non-linear interactions. This study bridges this gap by developing and evaluating a novel hybrid forecasting framework that synergistically combines statistical and machine learning (ML) approaches. We hypothesize that while statistical models capture linear components, ML models excel at modeling non-linear residuals. Our methodology employs a comprehensive simulation study to systematically control data characteristics, alongside an empirical analysis of a real financial dataset from the Dhaka Stock Exchange. Results demonstrate that hybrid models, particularly SVR-ANN and SVR-ETS, significantly outperform individual and other hybrid models across all accuracy metrics (RMSE, MAE, MAPE, MASE). The simulation confirmed this superiority, with the top hybrids achieving a mean MASE of 0.701. This indicates that an ML model, especially SVR, is highly effective in modeling the complex residuals from a primary statistical forecast. We conclude that a hybrid paradigm integrating statistical and ML techniques offers a robust and superior solution for forecasting DTMS series, providing practitioners with evidence-based guidance for enhanced accuracy.