Analysis of Multistate Autoregressive Models

Jie Ding, Shahin Shahrampour, Kathryn Heal, Vahid Tarokh

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


In this paper, we consider the inference problem for a wide class of time-series models, referred to as multistate autoregressive models. The time series that we consider are composed of multiple epochs, each modeled by an autoregressive process. The number of epochs is unknown, and the transitions of states follow a Markov process of an unknown order. We propose an inference strategy that enables reliable and efficient offline analysis of this class of time series. The inference is carried out through a three-step approach: detecting the structural changes of the time series using a recently proposed multiwindow algorithm, identifying each segment as a state and selecting the most appropriate number of states, and estimating the Markov source based upon the symbolic sequence obtained from previous steps. We provide theoretical results and algorithms in order to facilitate the inference procedure described above. We demonstrate the accuracy, efficiency, and wide applicability of the proposed algorithms via an array of experiments using synthetic and real-world data.

Original languageEnglish (US)
Pages (from-to)2429-2440
Number of pages12
JournalIEEE Transactions on Signal Processing
Issue number9
StatePublished - May 1 2018

Bibliographical note

Funding Information:
Manuscript received May 29, 2017; revised October 14, 2017 and December 1, 2017; accepted February 8, 2018. Date of publication March 12, 2018; date of current version April 2, 2018. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Lei Huang. This work was supported by the Defense Advanced Research Projects Agency under Grant W911NF-14-1-0508 and Grant N66001-15-C-4028. (Corresponding author: Jie Ding.) J. Ding and V. Tarokh are with the Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708 USA (e-mail:, djrlthu@;

Publisher Copyright:
© 1991-2012 IEEE.


  • Consistency
  • multi-regime models
  • prediction
  • recurring patterns
  • time series


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