Generalized binary vector autoregressive processes

Abstract

Vector-valued extensions of univariate generalized binary auto-regressive (gbAR) processes are proposed that enable the joint modeling of serial and cross-sectional 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 (PM10, ‘fine dust’) alarm data observed at six monitoring stations in Stuttgart, Germany.