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LoFT-LLM: Low-Frequency Time-Series Forecasting with Large Language Models

Jiacheng You, Jingcheng Yang, Yuhang Xie, Zhongxuan Wu, Xiucheng Li, Feng Li, Pengjie Wang, Jian Xu, Bo Zheng, Xinyang Chen

TL;DR

LoFT-LLM tackles data-scarce time-series forecasting by separating the learning of low-frequency trends from high-frequency noise. It combines a Patch Low-Frequency forecasting Module (PLFM) with a residual high-frequency learner and a parameter-efficient LLM calibration module that injects domain knowledge via structured prompts. The key novelty is the Frequency Alignment Loss (FALoss) and STFT-inspired patchwise frequency learning, which stabilize training and improve long-term accuracy, especially in few-shot regimes. Empirical results on financial and solar-energy datasets show consistent improvements over strong baselines, validating the hybrid approach's effectiveness and interpretability in real-world settings.

Abstract

Time-series forecasting in real-world applications such as finance and energy often faces challenges due to limited training data and complex, noisy temporal dynamics. Existing deep forecasting models typically supervise predictions using full-length temporal windows, which include substantial high-frequency noise and obscure long-term trends. Moreover, auxiliary variables containing rich domain-specific information are often underutilized, especially in few-shot settings. To address these challenges, we propose LoFT-LLM, a frequency-aware forecasting pipeline that integrates low-frequency learning with semantic calibration via a large language model (LLM). Firstly, a Patch Low-Frequency forecasting Module (PLFM) extracts stable low-frequency trends from localized spectral patches. Secondly, a residual learner then models high-frequency variations. Finally, a fine-tuned LLM refines the predictions by incorporating auxiliary context and domain knowledge through structured natural language prompts. Extensive experiments on financial and energy datasets demonstrate that LoFT-LLM significantly outperforms strong baselines under both full-data and few-shot regimes, delivering superior accuracy, robustness, and interpretability.

LoFT-LLM: Low-Frequency Time-Series Forecasting with Large Language Models

TL;DR

LoFT-LLM tackles data-scarce time-series forecasting by separating the learning of low-frequency trends from high-frequency noise. It combines a Patch Low-Frequency forecasting Module (PLFM) with a residual high-frequency learner and a parameter-efficient LLM calibration module that injects domain knowledge via structured prompts. The key novelty is the Frequency Alignment Loss (FALoss) and STFT-inspired patchwise frequency learning, which stabilize training and improve long-term accuracy, especially in few-shot regimes. Empirical results on financial and solar-energy datasets show consistent improvements over strong baselines, validating the hybrid approach's effectiveness and interpretability in real-world settings.

Abstract

Time-series forecasting in real-world applications such as finance and energy often faces challenges due to limited training data and complex, noisy temporal dynamics. Existing deep forecasting models typically supervise predictions using full-length temporal windows, which include substantial high-frequency noise and obscure long-term trends. Moreover, auxiliary variables containing rich domain-specific information are often underutilized, especially in few-shot settings. To address these challenges, we propose LoFT-LLM, a frequency-aware forecasting pipeline that integrates low-frequency learning with semantic calibration via a large language model (LLM). Firstly, a Patch Low-Frequency forecasting Module (PLFM) extracts stable low-frequency trends from localized spectral patches. Secondly, a residual learner then models high-frequency variations. Finally, a fine-tuned LLM refines the predictions by incorporating auxiliary context and domain knowledge through structured natural language prompts. Extensive experiments on financial and energy datasets demonstrate that LoFT-LLM significantly outperforms strong baselines under both full-data and few-shot regimes, delivering superior accuracy, robustness, and interpretability.
Paper Structure (27 sections, 12 equations, 7 figures, 8 tables)

This paper contains 27 sections, 12 equations, 7 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Time Series Forecasting
  4. Large Language Models
  5. Frequency Modeling in Deep Learning.
  6. Method
  7. Frequency Alignment Loss
  8. Patch Low-Frequency Forecasting Module
  9. Residual Learning
  10. Domain Knowledge-Injection Module via LLM Calibration
  11. Experiments
  12. Experimental Setup
  13. Comparative Experiments
  14. Few-Shot Forecasting
  15. Ablation Study
  16. ...and 12 more sections

Figures (7)

  • Figure 1: LoFT-LLM training and inference pipeline. (a) Training the low-frequency learner (PLFM) using filtered ground truth. (b) Training the residual learner with PLFM fixed. (c) Fine-tuning the LLM using prompt constructed from both learners and auxiliary information. (d) Inference combines all modules to generate final predictions.
  • Figure 2: Overall architecture of LoFT-LLM. (a) Structure of the residual learner, consisting primarily of a configurable backbone predictor. (b) The main pipeline of the LoFT-LLM. (c) Internal architecture and PLFM. Components highlighted with red dashed boxes are used only during training.
  • Figure 3: Visualization of noisy time series and its low-pass filtered counterpart. The filtered signal highlights dominant low-frequency trends, which are used as supervision targets in our frequency-aware learning strategy.
  • Figure 4: Prompt example. <> and <> are task-specific configurations and calculated input statistics. A complete example of the prompt can be found in Appendix \ref{['app:prompt']}
  • Figure 5: An example of the input prompt used for LLM calibration on the FundAR dataset.
  • ...and 2 more figures