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 (PM₁₀, ‘fine dust’) alarm data observed at six monitoring stations in Stuttgart, Germany.

中文翻译：

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广义二元向量自回归过程

提出了单变量广义二元自回归 (gbAR) 过程的向量值 60 扩展，可以对多变量二元数据的串行和横截面 50 依赖性进行联合建模。由此产生的广义二元向量自回归 (gbVAR) 模型类是简约的、可很好地解释的，并且还允许对负相关性进行建模。我们提供平稳条件并推导出允许证明几何混合属性的移动平均类型表示。此外，我们推导出 gbVAR 过程的一般随机属性，包括转换概率的公式。特别是，经典的 Yule-Walker 方程有助于 gbVAR 模型中的参数估计。在模拟中，我们研究了估计性能，为了说明，₁₀，“细粉尘”）在德国斯图加特的六个监测站观察到的警报数据。