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Multivariate count autoregression. (English) Zbl 1456.62155

Linear and log-linear models are studied for multivariate count time series data with Poisson marginals. A copula function is introduced on a vector of associated continuous random variables. The conditions for ergodicity and stationarity are derived based on a perturbation approach in Markov chain theory and theory of weak dependence. Quasi-likelihood estimating functions are suggested that yield consistent and asymptotically normal estimators of model parameters. A limited simulation study and a real data example illustrate the results.

MSC:

62J12 Generalized linear models (logistic models)
62F12 Asymptotic properties of parametric estimators
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H12 Estimation in multivariate analysis
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