A Harmonious Convergence of Machine Learning and DWT - SARIMA for Time Series Forecasting

In complex time series prediction, multi - resolution feature coupling and noise sensitivity impede accuracy. To address this, this study innovatively combines DWT with the SARIMA model. It uses the Coiflet wavelet basis for three - level signal decomposition, establishing a “high-freq noise suppression, mid-freq period analysis, low-freq trend fitting” mechanism. This overcomes the limitations of traditional SARIMA in non - stationary series modeling and its noise-sensitivity issues. Experiments indicate that the hybrid framework reduces computational time compared to deep-learning models while maintaining performance, showing great application potential. For instance, in PM2.5 concentration prediction, it achieves an MAE of 5.31 μg/m<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> and an RMSE of 7.41 μg/m<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>, Compared with the solo SARIMA model, the MAE is reduced by 37.7% and the RMSE by 28.5%. Additionally, it cuts 46% of the RNN's computational time, thus providing a better solution for complex time series prediction.