Modeling and Estimation of Multivariate Discrete and Continuous Time Stationary Processes
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 c...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2020-09-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/article/10.3389/fams.2020.00043/full |
| _version_ | 1819037155485286400 |
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| author | Marko Voutilainen |
| author_facet | Marko Voutilainen |
| author_sort | Marko Voutilainen |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-21T08:16:55Z |
| format | Article |
| id | doaj.art-8e8601d02e1343f7b80282f6985867a2 |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-12-21T08:16:55Z |
| publishDate | 2020-09-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-8e8601d02e1343f7b80282f6985867a22022-12-21T19:10:33ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872020-09-01610.3389/fams.2020.00043509968Modeling and Estimation of Multivariate Discrete and Continuous Time Stationary ProcessesMarko VoutilainenIn 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.https://www.frontiersin.org/article/10.3389/fams.2020.00043/fulltime-series analysisstationary processescharacterizationmultivariate Ornstein-Uhlenbeck processesgeneralized Langevin equationalgebraic Riccati equations |
| spellingShingle | Marko Voutilainen Modeling and Estimation of Multivariate Discrete and Continuous Time Stationary Processes Frontiers in Applied Mathematics and Statistics time-series analysis stationary processes characterization multivariate Ornstein-Uhlenbeck processes generalized Langevin equation algebraic Riccati equations |
| title | Modeling and Estimation of Multivariate Discrete and Continuous Time Stationary Processes |
| title_full | Modeling and Estimation of Multivariate Discrete and Continuous Time Stationary Processes |
| title_fullStr | Modeling and Estimation of Multivariate Discrete and Continuous Time Stationary Processes |
| title_full_unstemmed | Modeling and Estimation of Multivariate Discrete and Continuous Time Stationary Processes |
| title_short | Modeling and Estimation of Multivariate Discrete and Continuous Time Stationary Processes |
| title_sort | modeling and estimation of multivariate discrete and continuous time stationary processes |
| topic | time-series analysis stationary processes characterization multivariate Ornstein-Uhlenbeck processes generalized Langevin equation algebraic Riccati equations |
| url | https://www.frontiersin.org/article/10.3389/fams.2020.00043/full |
| work_keys_str_mv | AT markovoutilainen modelingandestimationofmultivariatediscreteandcontinuoustimestationaryprocesses |