HADL Framework for Noise Resilient Long-Term Time Series Forecasting

TL;DR

The paper introduces HADL, a framework combining wavelet and cosine transforms with a low-rank prediction layer to enhance noise resilience and efficiency in long-term time series forecasting.

Contribution

It proposes a novel noise reduction and feature extraction method using DWT and DCT, along with a lightweight prediction layer, improving robustness and computational efficiency.

Findings

Achieves state-of-the-art performance on benchmark datasets.

Demonstrates robustness in high-noise and irregular pattern scenarios.

Reduces computational complexity significantly.

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.