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HADL Framework for Noise Resilient Long-Term Time Series Forecasting

Aditya Dey, Jonas Kusch, Fadi Al Machot

TL;DR

This paper proposes a novel framework that addresses challenges of temporal noise in extended lookback windows by integrating the Discrete Wavelet Transform and Discrete Cosine Transform to perform noise reduction and extract robust long-term features and introduces a lightweight low-rank linear prediction layer that not only reduces the influence of residual noise but also improves memory efficiency.

Abstract

Long-term time series forecasting is critical in domains such as finance, economics, and energy, where accurate and reliable predictions over extended horizons drive strategic decision-making. Despite the progress in machine learning-based models, the impact of temporal noise in extended lookback windows remains underexplored, often degrading model performance and computational efficiency. In this paper, we propose a novel framework that addresses these challenges by integrating the Discrete Wavelet Transform (DWT) and Discrete Cosine Transform (DCT) to perform noise reduction and extract robust long-term features. These transformations enable the separation of meaningful temporal patterns from noise in both the time and frequency domains. To complement this, we introduce a lightweight low-rank linear prediction layer that not only reduces the influence of residual noise but also improves memory efficiency. Our approach demonstrates competitive robustness to noisy input, significantly reduces computational complexity, and achieves competitive or state-of-the-art forecasting performance across diverse benchmark datasets. Extensive experiments reveal that the proposed framework is particularly effective in scenarios with high noise levels or irregular patterns, making it well suited for real-world forecasting tasks. The code is available in https://github.com/forgee-master/HADL.

HADL Framework for Noise Resilient Long-Term Time Series Forecasting

TL;DR

This paper proposes a novel framework that addresses challenges of temporal noise in extended lookback windows by integrating the Discrete Wavelet Transform and Discrete Cosine Transform to perform noise reduction and extract robust long-term features and introduces a lightweight low-rank linear prediction layer that not only reduces the influence of residual noise but also improves memory efficiency.

Abstract

Long-term time series forecasting is critical in domains such as finance, economics, and energy, where accurate and reliable predictions over extended horizons drive strategic decision-making. Despite the progress in machine learning-based models, the impact of temporal noise in extended lookback windows remains underexplored, often degrading model performance and computational efficiency. In this paper, we propose a novel framework that addresses these challenges by integrating the Discrete Wavelet Transform (DWT) and Discrete Cosine Transform (DCT) to perform noise reduction and extract robust long-term features. These transformations enable the separation of meaningful temporal patterns from noise in both the time and frequency domains. To complement this, we introduce a lightweight low-rank linear prediction layer that not only reduces the influence of residual noise but also improves memory efficiency. Our approach demonstrates competitive robustness to noisy input, significantly reduces computational complexity, and achieves competitive or state-of-the-art forecasting performance across diverse benchmark datasets. Extensive experiments reveal that the proposed framework is particularly effective in scenarios with high noise levels or irregular patterns, making it well suited for real-world forecasting tasks. The code is available in https://github.com/forgee-master/HADL.

Paper Structure

This paper contains 27 sections, 11 equations, 3 figures, 11 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. MLP-Based Models for Lightweight Forecasting
  4. Convolutional and Recurrent Neural Network Methods
  5. Transformer-based Models
  6. The Proposed Method
  7. Discrete Wavelet Transform
  8. Discrete Cosine Transform
  9. Low Rank Layer
  10. Key Features
  11. Experiments
  12. Results
  13. Ablation Studies and Analysis
  14. Effects of Haar Decomposition
  15. Effects of Low-Rank Layer
  16. ...and 12 more sections

Figures (3)

  • Figure 1: Illustration of the HADL architecture.
  • Figure 2: Heatmap plot of the Low-Rank Matrix for a lookback window $L=512$ and a prediction length $H=96$ in the HADL framework with (w/) and without (w/o) Discrete Cosine Transformation on the ETTh1 dataset.
  • Figure 3: Heatmap plot for HADL framework comparing the Standard Linear and Low-Rank Matrices for a lookback window $L=512$ and a prediction length $H=96$ for ETTh1 dataset. Bias is set to False.