FLDmamba: Integrating Fourier and Laplace Transform Decomposition with Mamba for Enhanced Time Series Prediction

-- Time series prediction, a crucial task across various domains, faces significant challenges due to the inherent complexities of time series data, including non-stationarity, multi-scale periodicity, and transient dynamics, particularly when tackling long-term predictions. While Transformer-based architectures have shown promise, their quadratic complexity with sequence length hinders their efficiency for long-term predictions. Meanwhile, they are susceptible to data noise issues in time series. This paper proposes a novel framework, FLDmamba (Fourier and Laplace Transform Decomposition Mamba), addressing these limitations. FLDmamba leverages the strengths of both Fourier and Laplace transforms to effectively capture both multi-scale periodicity, transient dynamics within time series data, and improve the robustness of the model to the data noise issue. Our extensive experiments demonstrate that FLDmamba achieves superior performance on time series prediction benchmarks, outperforming both Transformer-based and other Mamba-based architectures. IME series prediction, which forecasts the future values of a (multivariate) variable based on its historical values, finds its application across a wide range of fields. Examples include weather prediction [1, 2], power grid management [3], traffic prediction [4, 5, 6, 7, 8, 9, 10], and stock market [11, 12, 13, 14], to name just a few. Despite significant advancements in this domain, the inherent complexities of time series data, such as non-stationarity, multi-scale periodicity, intrinsic stochasticity, and noise, pose substantial challenges to existing predictive models in long-term prediction. Q. Zhang and S.M. Yiu are from the University of Hong Kong.