FreDF: Learning to Forecast in the Frequency Domain

FreDF: Learning to Forecast in the Frequency Domain

6 May 2025 | Hao Wang, Licheng Pan, Yuan Shen, Zhichao Chen, Degui Yang, Yifei Yang, Sen Zhang, Xinggao Liu, Haoxuan Li, Dacheng Tao
The paper "FreDF: Learning to Forecast in the Frequency Domain" addresses the challenge of label autocorrelation in time series forecasting, which biases the learning objective of the Direct Forecast (DF) paradigm. The DF paradigm, widely used in modern forecasting models, generates multi-step forecasts independently, assuming step-wise independence in the label sequence. However, this approach overlooks the label autocorrelation, leading to biased forecasts. To tackle this issue, the authors propose Frequency-enhanced Direct Forecast (FreDF), which aligns the forecast and label sequences in the frequency domain to mitigate label autocorrelation. By transforming the label sequence into the frequency domain using the Discrete Fourier Transform (DFT), FreDF reduces the autocorrelation and biases in the learning objective. The method is model-agnostic and compatible with various forecasting models, including Transformers and MLPs. Experiments on multiple datasets and models demonstrate that FreDF significantly improves the performance of forecasting models, particularly in long-term forecasting tasks. The paper also provides an ablative study to validate the effectiveness of FreDF's components and explores its adaptability to different forecasting models and domain transformations. Additionally, the authors analyze the hyperparameter sensitivity and demonstrate the sample efficiency of FreDF, showing that it achieves comparable performance with limited training data. Overall, FreDF offers a novel approach to enhance the accuracy and robustness of time series forecasting by effectively managing label autocorrelation.The paper "FreDF: Learning to Forecast in the Frequency Domain" addresses the challenge of label autocorrelation in time series forecasting, which biases the learning objective of the Direct Forecast (DF) paradigm. The DF paradigm, widely used in modern forecasting models, generates multi-step forecasts independently, assuming step-wise independence in the label sequence. However, this approach overlooks the label autocorrelation, leading to biased forecasts. To tackle this issue, the authors propose Frequency-enhanced Direct Forecast (FreDF), which aligns the forecast and label sequences in the frequency domain to mitigate label autocorrelation. By transforming the label sequence into the frequency domain using the Discrete Fourier Transform (DFT), FreDF reduces the autocorrelation and biases in the learning objective. The method is model-agnostic and compatible with various forecasting models, including Transformers and MLPs. Experiments on multiple datasets and models demonstrate that FreDF significantly improves the performance of forecasting models, particularly in long-term forecasting tasks. The paper also provides an ablative study to validate the effectiveness of FreDF's components and explores its adaptability to different forecasting models and domain transformations. Additionally, the authors analyze the hyperparameter sensitivity and demonstrate the sample efficiency of FreDF, showing that it achieves comparable performance with limited training data. Overall, FreDF offers a novel approach to enhance the accuracy and robustness of time series forecasting by effectively managing label autocorrelation.
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