Empirical Evaluation of Wavelet Filter and Wavelet Decomposition Level on Time Series Forecasting

Time series forecasting is essential for anticipating future outcomes and supporting decision-making, yet achieving high predictive accuracy remains challenging. Wavelet-based approaches, particularly the Maximal Overlap Discrete Wavelet Transform (MODWT), offer potential improvements, although limited studies have systematically compared wavelet filter types and decomposition levels. This study evaluates several wavelet filters and decomposition levels combined with ARIMA models across six datasets exhibiting varying temporal characteristics. Forecasting accuracy was measured using the Mean Absolute Error (MAE) and Symmetric Mean Absolute Percentage Error (SMAPE). For the datasets analyzed, the Haar filter yielded the lowest MAE and SMAPE values, a result supported by the Kruskal–Wallis test and Dunn's test, which indicated significant differences in accuracy across filters. In contrast, differences in decomposition levels were not statistically significant, suggesting that decomposition level played a limited role in forecasting performance within this dataset context. These findings provide empirical, dataset-specific evidence regarding filter selection in MODWT–ARIMA modeling and highlight the comparatively minor influence of decomposition level on forecasting accuracy.