Modeling Frequency Correlation to Achieve Better Long-Term Series Forecasting

Long-term time series prediction is of great value in finance, meteorology, and industry. The early mainstream frameworks are statistic-based models such as ARIMA and Moving Average. Such models were gradually replaced by deep learning models because they could not handle complex nonlinear relationships. Well-known deep models include RNN, LSTM, GRU, etc. However, these models exhibit limitations in capturing long-term temporal dependencies. The recent success of Transformer in natural language processing (NLP) has inspired their adaptation for time series forecasting. Their attention mechanism can model dependencies at arbitrary time steps, which is theoretically suitable for long-term prediction tasks. However, studies have shown that a simple MLP model can outperform Transformer-based approaches, which has led to renewed interest in MLP-based forecasting frameworks. A limitation of existing methods is that they mainly focus on time domain features and ignore frequency domain information. Although some studies have attempted to use frequency domain information, they examine single variables in isolation, and fail to capture frequency domain correlations across variables. To address these challenges, we propose a model based on cross-spectral entropy filtering and causal dilated pyramid convolution, called CSConv. Specifically, CSConv uses cross-spectral entropy for adaptive frequency-domain filtering, preserving multivariate joint spectral characteristics. In addition, CSConv includes a time-weighted causal dilated pyramid convolution, which captures multi-scale dependencies through dilation structures and temporal decay weights. The final prediction is achieved through an MLP-based architecture that decomposes trend, cyclical, and residual components. We validate the performance of CSConv on eight real-world datasets and compare the results with advanced baseline models. Experiments show that our model achieves competitive results on multiple evaluation metrics.