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ReNF: Rethinking the Design Space of Neural Long-Term Time Series Forecasters

Yihang Lu, Xianwei Meng, Enhong Chen

TL;DR

Boosted Direct Output (BDO), a streamlined paradigm that synergistically hybridizes the causal structure of Auto-Regressive with the stability of Direct Output with the stability of Direct Output, while implicitly realizing the principle of forecast combination within a single network is proposed.

Abstract

Neural Forecasters (NFs) are a cornerstone of Long-term Time Series Forecasting (LTSF). However, progress has been hampered by an overemphasis on architectural complexity at the expense of fundamental forecasting principles. In this work, we return to first principles to redesign the LTSF paradigm. We begin by introducing a Multiple Neural Forecasting Theorem that provides a theoretical basis for our approach. We propose Boosted Direct Output (BDO), a novel forecasting strategy that synergistically combines the advantages of both Auto-Regressive (AR) and Direct Output (DO). In addition, we stabilize the learning process by smoothly tracking the model's parameters. Extensive experiments show that these principled improvements enable a simple MLP to achieve state-of-the-art performance, outperforming recent, complex models in nearly all cases, without any specific considerations in the area. Finally, we empirically verify our theorem, establishing a dynamic performance bound and identifying promising directions for future research. The code for review is available at: .

ReNF: Rethinking the Design Space of Neural Long-Term Time Series Forecasters

TL;DR

Boosted Direct Output (BDO), a streamlined paradigm that synergistically hybridizes the causal structure of Auto-Regressive with the stability of Direct Output with the stability of Direct Output, while implicitly realizing the principle of forecast combination within a single network is proposed.

Abstract

Neural Forecasters (NFs) are a cornerstone of Long-term Time Series Forecasting (LTSF). However, progress has been hampered by an overemphasis on architectural complexity at the expense of fundamental forecasting principles. In this work, we return to first principles to redesign the LTSF paradigm. We begin by introducing a Multiple Neural Forecasting Theorem that provides a theoretical basis for our approach. We propose Boosted Direct Output (BDO), a novel forecasting strategy that synergistically combines the advantages of both Auto-Regressive (AR) and Direct Output (DO). In addition, we stabilize the learning process by smoothly tracking the model's parameters. Extensive experiments show that these principled improvements enable a simple MLP to achieve state-of-the-art performance, outperforming recent, complex models in nearly all cases, without any specific considerations in the area. Finally, we empirically verify our theorem, establishing a dynamic performance bound and identifying promising directions for future research. The code for review is available at: .

Paper Structure

This paper contains 27 sections, 1 theorem, 17 equations, 14 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Preliminaries
  4. Theoretical Motivation for Multiple Forecasts
  5. Novel Forecasting Paradigm
  6. Model Architecture
  7. Learning Objective
  8. Smoothing the learning for time series
  9. Experiment
  10. Main Result
  11. Ablation Study
  12. Empirical Evaluation of the Proposition
  13. conclusion
  14. Reproducibility statement
  15. Supplementary Material
  16. ...and 12 more sections

Key Result

Proposition 1

Given a NFM $\Phi(t_x, t_y, \theta, \gamma)$ and an observed time series $X_h=(x_1,x_2,\cdots,x_n)$ where each element $x_t$ is drawn from a true distribution $p_t(\mu_t, \sigma_t^2 )$ with mean $\mu$ and standard deviation $\sigma_t$. One can generate a series by $\Phi$: $\hat{Y}_f=(y_{1},y_{2},\cd

Figures (14)

  • Figure 1: Illustration of the MNFP.
  • Figure 2: Features of DO and BDO.
  • Figure 3: We make the forecast by applying independent heads on several non-overlapped chunks. The right figure shows the learning process in different settings.
  • Figure 4: Model Structure of ReNF.
  • Figure 5: Variation of valid and test loss before and after applying EMA smoothing. The valid loss and test loss are not consistent during the learning process of NFs without smoothing.
  • ...and 9 more figures

Theorems & Definitions (4)

  • Definition 1: Neural Forecasting Machine
  • Definition 2: Forecasting Task
  • Proposition 1: Multiple Neural Forecasting Proposition (MNFP)
  • Definition 3: Boost Direct Output (BDO)