TFMSNet: A time series forecasting framework with time–frequency analysis and multi-scale processing

Time series forecasting is crucial in various fields. When dealing with complex time series data, existing methods often focus on a single scale or overlook frequency domain information, leading to the loss of critical information. To address this, this paper proposes TFMSNet, a novel time series forecasting framework combining time–frequency analysis with multi-scale processing. The framework decomposes the data into seasonal and trend components. For the seasonal component, TFMSNet utilizes Discrete Wavelet Transform (DWT) to decompose the data into subsequences of different frequencies, combining this with patch-based encoding layers and Inverse DWT to finely capture and reconstruct time–frequency features. It then performs multi-scale analysis and forecasting. For the trend component, the framework achieves multi-resolution representations through downsampling and uses Multilayer Perceptrons (MLPs) for prediction. By integrating both frequency and time domain information and leveraging the multi-scale characteristics of the data, TFMSNet significantly enhances prediction accuracy and robustness. Across 70 results from seven datasets, TFMSNet achieves 48 best and 20 second-best results, demonstrating the best overall performance. © 2025 Elsevier Ltd