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

Abstract

Accurate forecasting of time series exhibiting damped trends with multiplicative seasonality (DTMS) is a critical yet challenging task, with significant implications for fields such as finance, environmental science, and supply chain management. This study evaluates and enhances forecasting performance by proposing a hybrid framework that integrates conventional statistical models with machine learning (ML) techniques, validated through both real-world and simulated data. We investigate the effectiveness of three widely used models: Autoregressive Integrated Moving Average (ARIMA), Exponential Smoothing State Space (ETS), and Artificial Neural Networks (ANN), using both real-world data from Renata PLC and simulated datasets. To address multiplicative seasonality inherent in DTMS data, we incorporate seasonal adjustment via Seasonal-Trend decomposition using LOESS (STL). Forecast accuracy is assessed through multiple criteria, including Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE).

Results indicate that for real data, the hybrid TBATS+ANN model achieves superior performance (RMSE = 143.39, MAE = 121.45, MAPE = 9.62) compared to other hybrid approaches. Conversely, in simulated environments, STL+ETS (RMSE = 958.56, MAE = 808.25, MAPE = 62.45) and ETS+ARIMA (RMSE = 1469.64, MAE = 1188.51, MAPE = 76.01) outperform other models in different scenarios. Moreover, ETS+ARIMA demonstrates robust forecasting for certain DTMS multiplicative seasonality conditions (RMSE = 1512.21, MAE = 1232.12, MAPE = 70.13) across real and simulated data, though TBATS+ANN consistently shows competitive or superior accuracy (RMSE = 1515.82, MAE = 1230.33, MAPE = 65.98).

The findings underscore the value of hybrid modeling frameworks, especially those combining state-of-the-art statistical and machine learning approaches, for capturing the nuanced dynamics of DTMS data. This study provides comprehensive insights into model selection and sequencing, facilitating enhanced forecasting accuracy in challenging time series contexts. The results have practical implications for industries reliant on time-sensitive forecasts under multiplicative seasonal influences, and contribute to advancing methodologies for predictive analytics in complex trend environments. Therefore, this research contributes to the broader discourse on time-series forecasting by addressing gaps in DTMS modeling, with implications for decision-making in volatile or seasonal domains.