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WEITS: A Wavelet-enhanced residual framework for interpretable time series forecasting

Ziyou Guo, Yan Sun, Tieru Wu

TL;DR

This paper presents WEITS, a frequency-aware deep learning framework that is highly interpretable and computationally efficient, and provides a general framework that can always seamlessly integrate with state-of-the-art approaches for time series forecast.

Abstract

Time series (TS) forecasting has been an unprecedentedly popular problem in recent years, with ubiquitous applications in both scientific and business fields. Various approaches have been introduced to time series analysis, including both statistical approaches and deep neural networks. Although neural network approaches have illustrated stronger ability of representation than statistical methods, they struggle to provide sufficient interpretablility, and can be too complicated to optimize. In this paper, we present WEITS, a frequency-aware deep learning framework that is highly interpretable and computationally efficient. Through multi-level wavelet decomposition, WEITS novelly infuses frequency analysis into a highly deep learning framework. Combined with a forward-backward residual architecture, it enjoys both high representation capability and statistical interpretability. Extensive experiments on real-world datasets have demonstrated competitive performance of our model, along with its additional advantage of high computation efficiency. Furthermore, WEITS provides a general framework that can always seamlessly integrate with state-of-the-art approaches for time series forecast.

WEITS: A Wavelet-enhanced residual framework for interpretable time series forecasting

TL;DR

This paper presents WEITS, a frequency-aware deep learning framework that is highly interpretable and computationally efficient, and provides a general framework that can always seamlessly integrate with state-of-the-art approaches for time series forecast.

Abstract

Time series (TS) forecasting has been an unprecedentedly popular problem in recent years, with ubiquitous applications in both scientific and business fields. Various approaches have been introduced to time series analysis, including both statistical approaches and deep neural networks. Although neural network approaches have illustrated stronger ability of representation than statistical methods, they struggle to provide sufficient interpretablility, and can be too complicated to optimize. In this paper, we present WEITS, a frequency-aware deep learning framework that is highly interpretable and computationally efficient. Through multi-level wavelet decomposition, WEITS novelly infuses frequency analysis into a highly deep learning framework. Combined with a forward-backward residual architecture, it enjoys both high representation capability and statistical interpretability. Extensive experiments on real-world datasets have demonstrated competitive performance of our model, along with its additional advantage of high computation efficiency. Furthermore, WEITS provides a general framework that can always seamlessly integrate with state-of-the-art approaches for time series forecast.
Paper Structure (33 sections, 14 equations, 5 figures, 9 tables)

This paper contains 33 sections, 14 equations, 5 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Summary of contributions
  3. Wavelet decomposition for interpretability
  4. Residual stacking with multi-resolution
  5. Generalizability of framework
  6. Related works
  7. Multilevel wavelet decomposition
  8. Neural forecasting
  9. Interpretable forecasting
  10. Methodology
  11. Overview: residual stacking with signal enhancement
  12. Signal enhancement: MDWD
  13. Multi-resolution sampling
  14. Building blocks of stacks
  15. Neural basis expansion
  16. ...and 18 more sections

Figures (5)

  • Figure 1: Main structure of WEITS. The input to each stack is the residual from the last stack infused with a corresponding sub-series from wavelet decomposition (MDWD). Then the input goes through a dilated convolutional layer to the stack component (DLC) which generates partial backcast and forecast of the series. The global forecast is generated by summing up stack forecasts.
  • Figure 2: Illustration of MDWD. In each level the series is decoupled into a high- and low-frequency sub-series.
  • Figure 3: WEITS can utilize multiple structures as convolutional components within each stack, including DCN, CNN and MaxPooling.
  • Figure 4: Structure illustration of FCN and Informer as stack component of WEITS.
  • Figure 5: Comparison of stack output from WEITS and N-Beats. WEITS provides an easily understandable stack output that shows both trends and volatility.

Theorems & Definitions (2)

  • proof
  • proof