# HADL Framework for Noise Resilient Long-Term Time Series Forecasting

arXiv: https://arxiv.org/abs/2502.10569 · HTML: https://mlsanity.com/paper/2502.10569/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 14 Feb 2025.

## Builds on (most cited first, 20 of 20)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [DyLoRA: Parameter Efficient Tuning of Pre-trained Models using Dynamic Search-Free Low-Rank Adaptation](https://mlsanity.com/paper/2210.07558/) (2022)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [TSMixer: Lightweight MLP-Mixer Model for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2306.09364/) (2023)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [SegRNN: Segment Recurrent Neural Network for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2308.11200/) (2023)
- [Fredformer: Frequency Debiased Transformer for Time Series Forecasting](https://mlsanity.com/paper/2406.09009/) (2024)
- [Low-rank lottery tickets: finding efficient low-rank neural networks via matrix differential equations](https://mlsanity.com/paper/2205.13571/) (2022)
- [LightCTS: A Lightweight Framework for Correlated Time Series Forecasting](https://mlsanity.com/paper/2302.11974/) (2023)
- [xLSTMTime : Long-term Time Series Forecasting With xLSTM](https://mlsanity.com/paper/2407.10240/) (2024)
- [Channel-Aware Low-Rank Adaptation in Time Series Forecasting](https://mlsanity.com/paper/2407.17246/) (2024)
- [A probabilistic forecast methodology for volatile electricity prices in the Australian National Electricity Market](https://mlsanity.com/paper/2311.07289/) (2023)

## Built on by (most cited first, 1 of 1)

- [Benchmarking M-LTSF: Frequency and Noise-Based Evaluation of Multivariate Long Time Series Forecasting Models](https://mlsanity.com/paper/2510.04900/) (2025)

## Abstract (arXiv)

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.