Modeling and Estimation of Multivariate Discrete and Continuous Time Stationary Processes

Marko Voutilainen*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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In this paper, we give an autoregressive model of order 1 type of characterization covering all multivariate strictly stationary processes indexed by the set of integers. Consequently, under square integrability, we derive continuous time algebraic Riccati equations for the parameter matrix of the characterization. This provides us with a natural way to define the corresponding estimator. In addition, we show that the estimator inherits consistency from autocovariances of the stationary process. Furthermore, the limiting distribution is given by a linear function of the limiting distribution of the autocovariances. We also present the corresponding existing results of the continuous time setting paralleling them to the discrete case treated in this paper.

Original languageEnglish
Article number43
Number of pages12
JournalFrontiers in Applied Mathematics and Statistics
Publication statusPublished - 17 Sep 2020
MoE publication typeA1 Journal article-refereed


  • algebraic Riccati equations
  • characterization
  • consistency
  • estimation
  • generalized Langevin equation
  • multivariate Ornstein-Uhlenbeck processes
  • stationary processes
  • time-series analysis


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