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Generalized binary vector autoregressive processes. (English) Zbl 1493.62527

Summary: Vector-valued-60 extensions of univariate generalized binary auto-regressive (gbAR) processes are proposed that enable the joint modeling of serial and cross-sectional-50 dependence of multi-variate binary data. The resulting class of generalized binary vector auto-regressive (gbVAR) models is parsimonious, nicely interpretable and allows also to model negative dependence. We provide stationarity conditions and derive moving-average-type representations that allow to prove geometric mixing properties. Furthermore, we derive general stochastic properties of gbVAR processes, including formulae for transition probabilities. In particular, classical Yule-Walker equations hold that facilitate parameter estimation in gbVAR models. In simulations, we investigate the estimation performance, and for illustration, we apply gbVAR models to particulate matter (\(\mathrm{PM}_10\), ‘fine dust’) alarm data observed at six monitoring stations in Stuttgart, Germany.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H12 Estimation in multivariate analysis
62F40 Bootstrap, jackknife and other resampling methods
62M20 Inference from stochastic processes and prediction
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