Time series foundation models (TSFMs) demonstrate impressive zero-shot performance for time series forecasting. However, an important yet underexplored challenge is how to effectively finetune TSFMs on specific downstream tasks. While naive finetuning can yield performance gains, we argue that it falls short of fully leveraging TSFMs' capabilities, often resulting in overfitting and suboptimal performance. Given the diverse temporal patterns across sampling scales and the inherent multi-scale forecasting capabilities of TSFMs, we adopt a causal perspective to analyze finetuning process, through which we highlight the critical importance of explicitly modeling multiple scales and reveal the shortcomings of naive approaches. Focusing on encoder-based TSFMs, we propose Multiscale finetuning (MSFT), a simple yet general framework that explicitly integrates multi-scale modeling into the finetuning process. Experimental results on three different backbones (Moirai, Moment and Units) demonstrate that TSFMs finetuned with MSFT not only outperform naive and typical parameter efficient finetuning methods but also surpass state-of-the-art deep learning methods. Codes are available at https://github.com/zqiao11/MSFT.

Discrete Token Modeling (DTM), which employs vector quantization techniques, has demonstrated remarkable success in modeling non-natural language modalities, particularly in time series generation. While our prior work SDformer established the first DTM-based framework to achieve state-of-the-art performance in this domain, two critical limitations persist in existing DTM approaches: 1) their inability to capture multi-scale temporal patterns inherent to complex time series data, and 2) the absence of theoretical foundations to guide model optimization. To address these challenges, we proposes a novel multi-scale DTM-based time series generation method, called Multi-Scale Discrete Transformer (MSDformer). MSDformer employs a multi-scale time series tokenizer to learn discrete token representations at multiple scales, which jointly characterize the complex nature of time series data. Subsequently, MSDformer applies a multi-scale autoregressive token modeling technique to capture the multi-scale patterns of time series within the discrete latent space. Theoretically, we validate the effectiveness of the DTM method and the rationality of MSDformer through the rate-distortion theorem. Comprehensive experiments demonstrate that MSDformer significantly outperforms state-of-the-art methods. Both theoretical analysis and experimental results demonstrate that incorporating multi-scale information and modeling multi-scale patterns can substantially enhance the quality of generated time series in DTM-based approaches. The code will be released upon acceptance.

Transformer-based models have achieved some success in time series forecasting. Existing methods mainly model time series from limited or fixed scales, making it challenging to capture different characteristics spanning various scales. In this paper, we propose multi-scale transformers with adaptive pathways (Pathformer). The proposed Transformer integrates both temporal resolution and temporal distance for multi-scale modeling. Multi-scale division divides the time series into different temporal resolutions using patches of various sizes. Based on the division of each scale, dual attention is performed over these patches to capture global correlations and local details as temporal dependencies. We further enrich the multi-scale transformer with adaptive pathways, which adaptively adjust the multi-scale modeling process based on the varying temporal dynamics in the input time series, improving the prediction accuracy and generalization of Pathformer. Extensive experiments on eleven real-world datasets demonstrate that Pathformer not only achieves state-of-the-art performance by surpassing all current models but also exhibits stronger generalization abilities under various transfer scenarios. Time series forecasting is an essential task for various industries, such as energy, finance, traffic, and cloud computing (Chen et al., 2012; Cirstea et al., 2022b; Qin et al., 2023; Pan et al., 2023). Motivated by its widespread application in sequence modeling and impressive success in various fields such as CV and NLP (Dosovitskiy et al., 2021; Brown et al., 2020), Transformer (Vaswani et al., 2017) receives emerging attention in time series (Wu et al., 2021; Liu et al., 2022c).