D-PAD: Deep-Shallow Multi-Frequency Patterns Disentangling for Time Series Forecasting

TL;DR

D-PAD, a deep-shallow multi-frequency patterns disentangling neural network for time series forecasting achieves the state-of-the-art performance, outperforming the best baseline by an average of 9.48% and 7.15% in MSE and MAE, respectively.

Abstract

In time series forecasting, effectively disentangling intricate temporal patterns is crucial. While recent works endeavor to combine decomposition techniques with deep learning, multiple frequencies may still be mixed in the decomposed components, e.g., trend and seasonal. Furthermore, frequency domain analysis methods, e.g., Fourier and wavelet transforms, have limitations in resolution in the time domain and adaptability. In this paper, we propose D-PAD, a deep-shallow multi-frequency patterns disentangling neural network for time series forecasting. Specifically, a multi-component decomposing (MCD) block is introduced to decompose the series into components with different frequency ranges, corresponding to the "shallow" aspect. A decomposition-reconstruction-decomposition (D-R-D) module is proposed to progressively extract the information of frequencies mixed in the components, corresponding to the "deep" aspect. After that, an interaction and fusion (IF) module is used to further analyze the components. Extensive experiments on seven real-world datasets demonstrate that D-PAD achieves the state-of-the-art performance, outperforming the best baseline by an average of 9.48% and 7.15% in MSE and MAE, respectively.

Figures (7)

• Figure 1: Overview of D-PAD. (a) D-PAD is primarily composed of two parts, i.e., the D-R-D module and the interaction and fusion (IF) module. (b) The D-R block decomposes a series into multiple components and reconstructs them into two new series. (c) BGG is the combination of convolutions and projections, which generates $\mathbf{Q}$ and $\mathbf{K}$ to guide the branch selection for each component. (Best viewed in color).
• Figure 2: MCD block and its diagram. (a) The core of the MCD block is MEMD, which includes the iterative morphological empirical mode decomposition process (EMP). (b) The mathematical morphology is employed to calculate and draw upper and lower envelope curves in MEMD. (Best viewed in color).
• Figure 3: Results of D-PAD with different lookback window sizes of long-term forecasting ($H=720$) on ETT datasets.
• Figure 4: Results of models with different numbers of levels on ETT and Weather datasets.
• Figure 5: Visualization of the representations of different components on ETTh1 dataset from three views.