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We introduce Sundial, a family of native, flexible, and scalable time series foundation models. To predict the next-patch's distribution, we propose a TimeFlow Loss based on flow-matching, which facilitates native pre-training of Transformers on time series without discrete tokenization. Conditioned on arbitrary-length time series, our model is pre-trained without specifying any prior distribution and can generate multiple probable predictions, achieving flexibility in representation learning beyond using parametric densities. Towards time series foundation models, we leverage minimal but crucial adaptations of Transformers and curate TimeBench with 1 trillion time points, comprising mostly real-world datasets and synthetic data. By mitigating mode collapse through TimeFlow Loss, we pre-train a family of Sundial models on TimeBench, which exhibit unprecedented model capacity and generalization performance on zero-shot forecasting. In addition to presenting good scaling behavior, Sundial achieves new state-of-the-art on both point forecasting and probabilistic forecasting benchmarks. We believe that Sundial's pioneering generative paradigm will facilitate a wide variety of forecasting scenarios.

We present Timer-XL, a causal Transformer for unified time series forecasting. To uniformly predict multidimensional time series, we generalize next token prediction, predominantly adopted for 1D token sequences, to multivariate next token prediction. The paradigm formulates various forecasting tasks as a long-context prediction problem. We opt for decoder-only Transformers that capture causal dependencies from varying-length contexts for unified forecasting, making predictions on non-stationary univariate time series, multivariate series with complicated dynamics and correlations, as well as covariate-informed contexts that include exogenous variables. Technically, we propose a universal TimeAttention to capture fine-grained intra- and inter-series dependencies of flattened time series tokens (patches), which is further enhanced by deft position embedding for temporal causality and variable equivalence. Timer-XL achieves state-of-the-art performance across task-specific forecasting benchmarks through a unified approach. Based on large-scale pre-training, Timer-XL achieves state-of-the-art zero-shot performance, making it a promising architecture for pre-trained time series models. Code is available at this repository: https://github.com/thuml/Timer-XL.

Deep learning has contributed remarkably to the advancement of time series analysis. Still, deep models can encounter performance bottlenecks in real-world data-scarce scenarios, which can be concealed due to the performance saturation with small models on current benchmarks. Meanwhile, large models have demonstrated great powers in these scenarios through large-scale pre-training. Continuous progress has been achieved with the emergence of large language models, exhibiting unprecedented abilities such as few-shot generalization, scalability, and task generality, which are however absent in small deep models. To change the status quo of training scenario-specific small models from scratch, this paper aims at the early development of large time series models (LTSM). During pre-training, we curate large-scale datasets with up to 1 billion time points, unify heterogeneous time series into single-series sequence (S3) format, and develop the GPT-style architecture toward LTSMs. To meet diverse application needs, we convert forecasting, imputation, and anomaly detection of time series into a unified generative task. The outcome of this study is a Time Series Transformer (Timer), which is generative pre-trained by next token prediction and adapted to various downstream tasks with promising capabilities as an LTSM. Code and datasets are available at: https://github.com/thuml/Large-Time-Series-Model.

Foundation models of time series have not been fully developed due to the limited availability of time series corpora and the underexploration of scalable pre-training. Based on the similar sequential formulation of time series and natural language, increasing research demonstrates the feasibility of leveraging large language models (LLM) for time series. Nevertheless, the inherent autoregressive property and decoder-only architecture of LLMs have not been fully considered, resulting in insufficient utilization of LLM abilities. To fully revitalize the general-purpose token transition and multi-step generation capability of large language models, we propose AutoTimes to repurpose LLMs as autoregressive time series forecasters, which projects time series into the embedding space of language tokens and autoregressively generates future predictions with arbitrary lengths. Compatible with any decoder-only LLMs, the consequent forecaster exhibits the flexibility of the lookback length and scalability with larger LLMs. Further, we formulate time series as prompts, extending the context for prediction beyond the lookback window, termed in-context forecasting. By introducing LLM-embedded textual timestamps, AutoTimes can utilize chronological information to align multivariate time series. Empirically, AutoTimes achieves state-of-the-art with 0.1% trainable parameters and over $5\times$ training/inference speedup compared to advanced LLM-based forecasters. Code is available at this repository: https://github.com/thuml/AutoTimes.

With the wide application of time series databases (TSDBs) in big data fields like cluster monitoring and industrial IoT, there have been developed a number of TSDBs for time series data management. Different TSDBs have test reports comparing themselves with other databases to show their advantages, but the comparisons are typically based on their own tools without using a common well-recognized test framework. To the best of our knowledge, there is no mature TSDB benchmark either. With the goal of establishing a standard of evaluating TSDB systems, we present the IoTDB-Benchmark framework, specifically designed for TSDB and IoT application scenarios. We pay close attention to some special data ingestion scenarios and summarize 10 basic queries types. We use this benchmark to compare four TSDB systems: InfluxDB, OpenTSDB, KairosDB and TimescaleDB. Our benchmark framework/tool not only measures performance metrics but also takes system resource consumption into consideration.

Cassandra is a popular structured storage system with high-performance, scalability and high availability, and is usually used to store data that has some sortable attributes. When deploying and configuring Cassandra, it is important to design a suitable schema of column families for accelerating the target queries. However, one schema is only suitable for a part of queries, and leaves other queries with high latency. In this paper, we propose a new replica mechanism, called heterogeneous replica, to reduce the query latency greatly while ensuring high write throughput and data recovery. With this replica mechanism, different replica has the same dataset while having different serialization on disk. By implementing the heterogeneous replica mechanism on Cassandra, we show that the read performance of Cassandra can be improved by two orders of magnitude with TPC-H data set., Comment: 6 pages