A Markov-switching hidden heterogeneous network autoregressive model for multivariate time series data with multimodality

Abstract

Multivariate networked time series data are ubiquitous in many applications, where multiple variables of interest are sequentially collected over time for each vertex as multivariate time series. Data of different vertices may have heterogeneous influence on each other through the network topology. These time series may usually exhibit multimodal marginal distributions, due to complex system variations. In this article, we propose a novel approach for such data modeling. In particular, we assume that each vertex has multiple latent states and exhibits state-switching behaviors according to a Markov process. The multivariate time series of each vertex depend on a defined latent effect variable influenced by both its own latent state and the latent effects of its neighbors through a heterogeneous network autoregressive model according to the network topology. Furthermore, the influence of some exogenous covariates on the time series can also be incorporated in the model. Some model properties are discussed, and a variational EM algorithm is proposed for model parameter estimation and state inference. Extensive synthetic experiments and a real-world case study demonstrate the effectiveness and applicability of the proposed model.

Keywords:

• Networked time series data
• hidden Markov model
• multimodality
• regime-switching model
• variational EM

Acknowledgments

We are grateful to the department editor, the associate editor, and three anonymous referees for very helpful comments and suggestions, which have significantly improved the quality of this paper.

Additional information

Funding

This paper was supported by the NSFC Grant 71932006, 71901131, and 72271138, the BNSF Grant 9222014, the ASFC Grant 2020Z063058001, and the Tsinghua University Intelligent Logistics & Supply Chain Research Center Grant THUCSL20182911756-001.

Notes on contributors

Wanshan Li

Wanshan Li is a PhD candidate in Department of Industrial Engineering, Tsinghua University. She received her BEng degree from Shandong University in 2016. Her research interest include statistical modelling and maintenance scheduling for networked systems.

Chen Zhang

Chen Zhang is an associate professor in Department of Industrial Engineering, Tsinghua University. She received her PhD degree from National University of Singapore in 2017, and her BEng degree from Tianjin University in 2012. Her research interests include developing methodologies and algorithms for complex or large-scale systems with multivariate or highdimensional data.