On Multivariate Singular Spectrum Analysis: Tensor and Matrix Variants

• 成果类型: Article; Early Access
• 署名作者: Agarwal, Anish; Alomar, Abdullah; Shah, Devavrat
• 署名单位: Columbia University; Massachusetts Institute of Technology (MIT)
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2023.0060
• 发表日期: 2026-06-30
• 关键词: singular spectrum analysis; spatio-temporal factor model; number; models

摘要

We introduce and analyze two extensions of singular spectrum analysis (SSA) to the multivariate setting: a new variant of the well-known matrix-based method (mSSA) and a novel tensor-based approach (tSSA). Under a spatio-temporal factor model, we establish prediction-error guarantees for mSSA for both imputation and out-of-sample forecasting. By exploiting both spatial and temporal structure, mSSA achieves better rates than univariate SSA and standard matrix estimation methods. The out-of-sample forecasting result of mSSA could be of independent interest for online learning under a spatio-temporal factor model. For tSSA, we characterize its imputation mean squared error and showcase its better sample complexity, compared with mSSA, for certain regimes of N and T. We establish that our spatio-temporal model admits a broad range of time series dynamics including harmonics, polynomials, differentiable periodic functions, and Ho & uml;lder continuous functions. This is further illustrated via the Hankel calculus, which establishes that the set of time series the model represents is closed under component-wise addition and multiplication. Empirically, on benchmark data sets, mSSA performs competitively with state-of-the-art neural-network time series methods (e.g., DeepAR, long short-term memory) and significantly outperforms classical methods such as vector autoregression (VAR). Consistent with our theory, tSSA achieves improved imputation performance over mSSA in certain regimes of N and T. Finally, we introduce and analyze an additional variant of SSA to estimate the time-varying variance of a time series. To our knowledge, this is the first result providing provable finite-sample performance guarantees for estimating the time-varying variance of a time series.