FCP-Former: Enhancing Long-Term Multivariate Time Series Forecasting with Frequency Compensation

Long-term multivariate time series forecasting is crucial for real-world applications, including energy consumption, traffic flow, healthcare, and finance. Usually, some statistical approaches are used for predicting future observations based on historical temporal data. Recently, transformer-based models with patch mechanisms have demonstrated significant potential in enhancing computational efficiency. However, their inability to fully capture intra-patch temporal dependencies often limits the accuracy of predictions. To address this issue, we propose the Frequency Compensation Patch-wise transFormer (FCP-Former), which integrates a frequency compensation layer into the patching mechanism. This layer extracts frequency-domain features via Fast Fourier Transform (FFT) and incorporates them into patched data, thereby enriching patch representations and mitigating intra-patch information loss. To verify the feasibility of this model, FCP-Former was conducted on eight benchmark datasets via PyTorch 2.4.0 and trained on an NVIDIA RTX 4090 GPU (Santa Clara, CA, USA). Results demonstrate that FCP-Former 48 optimal experiment results and 17 suboptimal experiment results across all datasets. Especially on the ETTh1 dataset, it achieves an average MSE of 0.437 and an average MAE of 0.430, while on the Electricity dataset, it achieves an average MSE of 0.186 and an average MAE of 0.277. This demonstrates that FCP-Former has better forecasting accuracy and a superior ability to capture periodic and trend patterns.