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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Multivariate count autoregression
AU - Fokianos, Konstantinos
AU - Stove, Bard
AU - Tjostheim, Dag
AU - Doukhan, Paul
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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.
AB - 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.
U2 - 10.3150/19-BEJ1132
DO - 10.3150/19-BEJ1132
M3 - Journal article
VL - 26
SP - 471
EP - 499
JO - Bernoulli
JF - Bernoulli
SN - 1350-7265
IS - 1
ER -