Time series analysis plays a critical role in numerous applications, supporting tasks such as forecasting, classification, anomaly detection, and imputation. In this work, we present the time series pattern machine (TSPM), a model designed to excel in a broad range of time series tasks through powerful representation and pattern extraction capabilities. Traditional time series models often struggle to capture universal patterns, limiting their effectiveness across diverse tasks. To address this, we define multiple scales in the time domain and various resolutions in the frequency domain, employing various mixing strategies to extract intricate, task-adaptive time series patterns. Specifically, we introduce TimeMixer++, a general-purpose TSPM that processes multi-scale time series using (1) multi-resolution time imaging (MRTI), (2) time image decomposition (TID), (3) multi-scale mixing (MCM), and (4) multi-resolution mixing (MRM) to extract comprehensive temporal patterns. MRTI transforms multi-scale time series into multi-resolution time images, capturing patterns across both temporal and frequency domains. TID leverages dual-axis attention to extract seasonal and trend patterns, while MCM hierarchically aggregates these patterns across scales. MRM adaptively integrates all representations across resolutions. TimeMixer++ achieves state-of-the-art performance across 8 time series analytical tasks, consistently surpassing both general-purpose and task-specific models. Our work marks a promising step toward the next generation of TSPMs, paving the way for further advancements in time series analysis.

Deep learning for time series forecasting has seen significant advancements over the past decades. However, despite the success of large-scale pre-training in language and vision domains, pre-trained time series models remain limited in scale and operate at a high cost, hindering the development of larger capable forecasting models in real-world applications. In response, we introduce Time-MoE, a scalable and unified architecture designed to pre-train larger, more capable forecasting foundation models while reducing inference costs. By leveraging a sparse mixture-of-experts (MoE) design, Time-MoE enhances computational efficiency by activating only a subset of networks for each prediction, reducing computational load while maintaining high model capacity. This allows Time-MoE to scale effectively without a corresponding increase in inference costs. Time-MoE comprises a family of decoder-only transformer models that operate in an auto-regressive manner and support flexible forecasting horizons with varying input context lengths. We pre-trained these models on our newly introduced large-scale data Time-300B, which spans over 9 domains and encompassing over 300 billion time points. For the first time, we scaled a time series foundation model up to 2.4 billion parameters, achieving significantly improved forecasting precision. Our results validate the applicability of scaling laws for training tokens and model size in the context of time series forecasting. Compared to dense models with the same number of activated parameters or equivalent computation budgets, our models consistently outperform them by large margin. These advancements position Time-MoE as a state-of-the-art solution for tackling real-world time series forecasting challenges with superior capability, efficiency, and flexibility. Code is available at https://github.com/Time-MoE/Time-MoE

Many real-world applications contain data in the form of multivariate time series (TS) with the hierarchical structure, where classic methods forecasting each TS independently are inadequate for coherency (i.e., satisfying the hierarchical aggregation constraints).Furthermore, the discrepancies between statistical properties of different levels can be huge, exacerbated by non-Gaussian distributions and non-linear correlations.In this paper, we propose a novel end-to-end hierarchical TS forecasting model, i.e., a Flow-based Reconcile Transformer (FRT).FRT employs a conditional normalizing flow-based autoregressive transformer, to represent complex data distribution, while simultaneously reconciling the forecasts to ensure coherency.Go beyond other state-of-the-art methods, FRT accomplishes forecasting and reconciliation simultaneously, while avoiding any post-processing steps.Moreover, FRT is a deep model that does not rely on any strong assumptions such as unbiased estimates or Gaussian distribution.Our experiments are conducted on four real-world hierarchical datasets from different industrial domains (three public ones and a dataset from the application servers of our company's data center) and the results demonstrate the efficacy of our proposed method.Our method has been implemented extensively within the production environments of a prominent global payment company.It has emerged as a cornerstone for workload forecasting within their data center and plays a critical role in the optimization of cloud computing resource allocation across * Both authors contributed equally to this research.