Time Series Forecasting as Reasoning: A Slow-Thinking Approach with Reinforced LLMs

To advance time series forecasting (TSF), various methods have been proposed to improve prediction accuracy, evolving from statistical techniques to data-driven deep learning architectures. Despite their effectiveness, most existing methods still adhere to a fast thinking paradigm-relying on extracting historical patterns and mapping them to future values as their core modeling philosophy, lacking an explicit thinking process that incorporates intermediate time series reasoning. Meanwhile, emerging slow-thinking LLMs (e.g., OpenAI-o1) have shown remarkable multi-step reasoning capabilities, offering an alternative way to overcome these issues. However, prompt engineering alone presents several limitations - including high computational cost, privacy risks, and limited capacity for in-depth domain-specific time series reasoning. To address these limitations, a more promising approach is to train LLMs to develop slow thinking capabilities and acquire strong time series reasoning skills. For this purpose, we propose Time-R1, a two-stage reinforcement fine-tuning framework designed to enhance multi-step reasoning ability of LLMs for time series forecasting. Specifically, the first stage conducts supervised fine-tuning for warmup adaptation, while the second stage employs reinforcement learning to improve the model's generalization ability. Particularly, we design a fine-grained multi-objective reward specifically for time series forecasting, and then introduce GRIP (group-based relative importance for policy optimization), which leverages non-uniform sampling to further encourage and optimize the model's exploration of effective reasoning paths. Experiments demonstrate that Time-R1 significantly improves forecast performance across diverse datasets.

FDF: Flexible Decoupled Framework for Time Series Forecasting with Conditional Denoising and Polynomial Modeling

Time series forecasting is vital in numerous web applications, influencing critical decision-making across industries. While diffusion models have recently gained increasing popularity for this task, we argue they suffer from a significant drawback: indiscriminate noise addition to the original time series followed by denoising, which can obscure underlying dynamic evolving trend and complicate forecasting. To address this limitation, we propose a novel flexible decoupled framework (FDF) that learns high-quality time series representations for enhanced forecasting performance. A key characteristic of our approach leverages the inherent inductive bias of time series data by decomposing it into trend and seasonal components, each modeled separately to enable decoupled analysis and modeling. Specifically, we propose an innovative Conditional Denoising Seasonal Module (CDSM) within the diffusion model, which leverages statistical information from the historical window to conditionally model the complex seasonal component. Notably, we incorporate a Polynomial Trend Module (PTM) to effectively capture the smooth trend component, thereby enhancing the model's ability to represent temporal dependencies. Extensive experiments validate the effectiveness of our framework, demonstrating superior performance over existing methods and higlighting its flexibility in time series forecasting. We hope our work can bring a new perspective for time series forecasting. We intend to make our code publicly available as open-source in the future.

Diffusion Auto-regressive Transformer for Effective Self-supervised Time Series Forecasting

Self-supervised learning has become a popular and effective approach for enhancing time series forecasting, enabling models to learn universal representations from unlabeled data. However, effectively capturing both the global sequence dependence and local detail features within time series data remains challenging. To address this, we propose a novel generative self-supervised method called TimeDART, denoting Diffusion Auto-regressive Transformer for Time series forecasting. In TimeDART, we treat time series patches as basic modeling units. Specifically, we employ an self-attention based Transformer encoder to model the dependencies of inter-patches. Additionally, we introduce diffusion and denoising mechanisms to capture the detail locality features of intra-patch. Notably, we design a cross-attention-based denoising decoder that allows for adjustable optimization difficulty in the self-supervised task, facilitating more effective self-supervised pre-training. Furthermore, the entire model is optimized in an auto-regressive manner to obtain transferable representations. Extensive experiments demonstrate that TimeDART achieves state-of-the-art fine-tuning performance compared to the most advanced competitive methods in forecasting tasks. Our code is publicly available at https://github.com/Melmaphother/TimeDART.