Can Slow-thinking LLMs Reason Over Time? Empirical Studies in Time Series Forecasting

Time series forecasting (TSF) is a fundamental and widely studied task, spanning methods from classical statistical approaches to modern deep learning and multimodal language modeling. Despite their effectiveness, these methods often follow a fast thinking paradigm emphasizing pattern extraction and direct value mapping, while overlooking explicit reasoning over temporal dynamics and contextual dependencies. Meanwhile, emerging slow-thinking LLMs (e.g., ChatGPT-o1, DeepSeek-R1) have demonstrated impressive multi-step reasoning capabilities across diverse domains, suggesting a new opportunity for reframing TSF as a structured reasoning task. This motivates a key question: can slow-thinking LLMs effectively reason over temporal patterns to support time series forecasting, even in zero-shot manner? To investigate this, in this paper, we propose TimeReasoner, an extensive empirical study that formulates TSF as a conditional reasoning task. We design a series of prompting strategies to elicit inference-time reasoning from pretrained slow-thinking LLMs and evaluate their performance across diverse TSF benchmarks. Our findings reveal that slow-thinking LLMs exhibit non-trivial zero-shot forecasting capabilities, especially in capturing high-level trends and contextual shifts. While preliminary, our study surfaces important insights into the reasoning behaviors of LLMs in temporal domains highlighting both their potential and limitations. We hope this work catalyzes further research into reasoning-based forecasting paradigms and paves the way toward more interpretable and generalizable TSF frameworks.

Binary Cumulative Encoding meets Time Series Forecasting

Recent studies in time series forecasting have explored formulating regression via classification task. By discretizing the continuous target space into bins and predicting over a fixed set of classes, these approaches benefit from stable training, robust uncertainty modeling, and compatibility with modern deep learning architectures. However, most existing methods rely on one-hot encoding that ignores the inherent ordinal structure of the underlying values. As a result, they fail to provide information about the relative distance between predicted and true values during training. In this paper, we propose to address this limitation by introducing binary cumulative encoding (BCE), that represents scalar targets into monotonic binary vectors. This encoding implicitly preserves order and magnitude information, allowing the model to learn distance-aware representations while still operating within a classification framework. We propose a convolutional neural network architecture specifically designed for BCE, incorporating residual and dilated convolutions to enable fast and expressive temporal modeling. Through extensive experiments on benchmark forecasting datasets, we show that our approach outperforms widely used methods in both point and probabilistic forecasting, while requiring fewer parameters and enabling faster training.

Timing is important: Risk-aware Fund Allocation based on Time-Series Forecasting

Fund allocation has been an increasingly important problem in the financial domain. In reality, we aim to allocate the funds to buy certain assets within a certain future period. Naive solutions such as prediction-only or Predict-then-Optimize approaches suffer from goal mismatch. Additionally, the introduction of the SOTA time series forecasting model inevitably introduces additional uncertainty in the predicted result. To solve both problems mentioned above, we introduce a Risk-aware Time-Series Predict-and-Allocate (RTS-PnO) framework, which holds no prior assumption on the forecasting models. Such a framework contains three features: (i) end-to-end training with objective alignment measurement, (ii) adaptive forecasting uncertainty calibration, and (iii) agnostic towards forecasting models. The evaluation of RTS-PnO is conducted over both online and offline experiments. For offline experiments, eight datasets from three categories of financial applications are used: Currency, Stock, and Cryptos. RTS-PnO consistently outperforms other competitive baselines. The online experiment is conducted on the Cross-Border Payment business at FiT, Tencent, and an 8.4\% decrease in regret is witnessed when compared with the product-line approach. The code for the offline experiment is available at https://github.com/fuyuanlyu/RTS-PnO.

Multi-Modal View Enhanced Large Vision Models for Long-Term Time Series Forecasting

Time series, typically represented as numerical sequences, can also be transformed into images and texts, offering multi-modal views (MMVs) of the same underlying signal. These MMVs can reveal complementary patterns and enable the use of powerful pre-trained large models, such as large vision models (LVMs), for long-term time series forecasting (LTSF). However, as we identified in this work, applying LVMs to LTSF poses an inductive bias towards "forecasting periods". To harness this bias, we propose DMMV, a novel decomposition-based multi-modal view framework that leverages trend-seasonal decomposition and a novel backcast residual based adaptive decomposition to integrate MMVs for LTSF. Comparative evaluations against 14 state-of-the-art (SOTA) models across diverse datasets show that DMMV outperforms single-view and existing multi-modal baselines, achieving the best mean squared error (MSE) on 6 out of 8 benchmark datasets.

$K^2$VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting

Probabilistic Time Series Forecasting (PTSF) plays a crucial role in decision-making across various fields, including economics, energy, and transportation. Most existing methods excell at short-term forecasting, while overlooking the hurdles of Long-term Probabilistic Time Series Forecasting (LPTSF). As the forecast horizon extends, the inherent nonlinear dynamics have a significant adverse effect on prediction accuracy, and make generative models inefficient by increasing the cost of each iteration. To overcome these limitations, we introduce $K^2$VAE, an efficient VAE-based generative model that leverages a KoopmanNet to transform nonlinear time series into a linear dynamical system, and devises a KalmanNet to refine predictions and model uncertainty in such linear system, which reduces error accumulation in long-term forecasting. Extensive experiments demonstrate that $K^2$VAE outperforms state-of-the-art methods in both short- and long-term PTSF, providing a more efficient and accurate solution.

Improving Time Series Forecasting via Instance-aware Post-hoc Revision

Time series forecasting plays a vital role in various real-world applications and has attracted significant attention in recent decades. While recent methods have achieved remarkable accuracy by incorporating advanced inductive biases and training strategies, we observe that instance-level variations remain a significant challenge. These variations--stemming from distribution shifts, missing data, and long-tail patterns--often lead to suboptimal forecasts for specific instances, even when overall performance appears strong. To address this issue, we propose a model-agnostic framework, PIR, designed to enhance forecasting performance through Post-forecasting Identification and Revision. Specifically, PIR first identifies biased forecasting instances by estimating their accuracy. Based on this, the framework revises the forecasts using contextual information, including covariates and historical time series, from both local and global perspectives in a post-processing fashion. Extensive experiments on real-world datasets with mainstream forecasting models demonstrate that PIR effectively mitigates instance-level errors and significantly improves forecasting reliability.

CrossLinear: Plug-and-Play Cross-Correlation Embedding for Time Series Forecasting with Exogenous Variables

Time series forecasting with exogenous variables is a critical emerging paradigm that presents unique challenges in modeling dependencies between variables. Traditional models often struggle to differentiate between endogenous and exogenous variables, leading to inefficiencies and overfitting. In this paper, we introduce CrossLinear, a novel Linear-based forecasting model that addresses these challenges by incorporating a plug-and-play cross-correlation embedding module. This lightweight module captures the dependencies between variables with minimal computational cost and seamlessly integrates into existing neural networks. Specifically, it captures time-invariant and direct variable dependencies while disregarding time-varying or indirect dependencies, thereby mitigating the risk of overfitting in dependency modeling and contributing to consistent performance improvements. Furthermore, CrossLinear employs patch-wise processing and a global linear head to effectively capture both short-term and long-term temporal dependencies, further improving its forecasting precision. Extensive experiments on 12 real-world datasets demonstrate that CrossLinear achieves superior performance in both short-term and long-term forecasting tasks. The ablation study underscores the effectiveness of the cross-correlation embedding module. Additionally, the generalizability of this module makes it a valuable plug-in for various forecasting tasks across different domains. Codes are available at https://github.com/mumiao2000/CrossLinear.

Multivariate de Bruijn Graphs: A Symbolic Graph Framework for Time Series Forecasting

Time series forecasting remains a challenging task for foundation models due to temporal heterogeneity, high dimensionality, and the lack of inherent symbolic structure. In this work, we propose DRAGON (Discrete Representation and Augmented Graph encoding Over deBruijN Graphs), a novel encoder that introduces Multivariate de Bruijn Graphs (MdBGs) to bridge the gap between symbolic representations and neural modeling. DRAGON discretizes continuous input sequences and maps them onto a fixed graph structure, enabling dynamic context recovery via graph-based attention. Integrated as an auxiliary module within a dual-branch architecture, DRAGON augments conventional CNN-based encoders with symbolic, structure-aware representations. All code developed for this study is available at: https://github.com/KurbanIntelligenceLab/MultdBG-Time-Series-Library

TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learning

In-context learning, the ability of large language models to perform tasks using only examples provided in the prompt, has recently been adapted for time series forecasting. This paradigm enables zero-shot prediction, where past values serve as context for forecasting future values, making powerful forecasting tools accessible to non-experts and increasing the performance when training data are scarce. Most existing zero-shot forecasting approaches rely on transformer architectures, which, despite their success in language, often fall short of expectations in time series forecasting, where recurrent models like LSTMs frequently have the edge. Conversely, while LSTMs are well-suited for time series modeling due to their state-tracking capabilities, they lack strong in-context learning abilities. We introduce TiRex that closes this gap by leveraging xLSTM, an enhanced LSTM with competitive in-context learning skills. Unlike transformers, state-space models, or parallelizable RNNs such as RWKV, TiRex retains state-tracking, a critical property for long-horizon forecasting. To further facilitate its state-tracking ability, we propose a training-time masking strategy called CPM. TiRex sets a new state of the art in zero-shot time series forecasting on the HuggingFace benchmarks GiftEval and Chronos-ZS, outperforming significantly larger models including TabPFN-TS (Prior Labs), Chronos Bolt (Amazon), TimesFM (Google), and Moirai (Salesforce) across both short- and long-term forecasts.

Are Data Embeddings effective in time series forecasting?

Time series forecasting plays a crucial role in many real-world applications, and numerous complex forecasting models have been proposed in recent years. Despite their architectural innovations, most state-of-the-art models report only marginal improvements -- typically just a few thousandths in standard error metrics. These models often incorporate complex data embedding layers to transform raw inputs into higher-dimensional representations to enhance accuracy. But are data embedding techniques actually effective in time series forecasting? Through extensive ablation studies across fifteen state-of-the-art models and four benchmark datasets, we find that removing data embedding layers from many state-of-the-art models does not degrade forecasting performance. In many cases, it improves both accuracy and computational efficiency. The gains from removing embedding layers often exceed the performance differences typically reported between competing models. Code available at: https://github.com/neuripsdataembedidng/DataEmbedding