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February 2020 Multivariate count autoregression
Konstantinos Fokianos, Bård Støve, Dag Tjøstheim, Paul Doukhan
Bernoulli 26(1): 471-499 (February 2020). DOI: 10.3150/19-BEJ1132

Abstract

We are studying linear and log-linear models for multivariate count time series data with Poisson marginals. For studying the properties of such processes we develop a novel conceptual framework which is based on copulas. Earlier contributions impose the copula on the joint distribution of the vector of counts by employing a continuous extension methodology. Instead we introduce a copula function on a vector of associated continuous random variables. This construction avoids conceptual difficulties related to the joint distribution of counts yet it keeps the properties of the Poisson process marginally. Furthermore, this construction can be employed for modeling multivariate count time series with other marginal count distributions. We employ Markov chain theory and the notion of weak dependence to study ergodicity and stationarity of the models we consider. Suitable estimating equations are suggested for estimating unknown model parameters. The large sample properties of the resulting estimators are studied in detail. The work concludes with some simulations and a real data example.

Citation

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Konstantinos Fokianos. Bård Støve. Dag Tjøstheim. Paul Doukhan. "Multivariate count autoregression." Bernoulli 26 (1) 471 - 499, February 2020. https://doi.org/10.3150/19-BEJ1132

Information

Received: 1 May 2017; Revised: 1 May 2019; Published: February 2020
First available in Project Euclid: 26 November 2019

zbMATH: 07140506
MathSciNet: MR4036041
Digital Object Identifier: 10.3150/19-BEJ1132

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

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Vol.26 • No. 1 • February 2020
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