We introduce a general class of autoregressive models for studying the dynamic of multivariate binary time series with stationary exogenous covariates. Using a high-level set of assumptions, we show that existence of a stationary path for such models is almost automatic and does not require parameter restrictions when the noise term is not compactly supported. We then study in details statistical inference in a dynamic version of a multivariate probit type model, as a particular case of our general construction. To avoid a complex likelihood optimization, we combine pseudo-likelihood and pairwise likelihood methods for which asymptotic results are obtained for a single path analysis and also for panel data, using ergodic theorems for multi-indexed partial sums. The latter scenario is particularly important for analyzing absence-presence of species in Ecology, a field where data are often collected from surveys at various locations. Our results also give a theoretical background for such models which are often used by the practitioners but without a probabilistic framework.

翻译：本文引入了一类通用的自回归模型，用于研究具有平稳外生协变量的多元二元时间序列的动态特性。通过采用一组高层次的假设，我们证明了当噪声项不具有紧支撑时，此类模型平稳路径的存在几乎是自动的，且无需参数限制。随后，我们详细研究了多元概率单位类型模型的动态版本中的统计推断问题，该模型是我们通用构建的一个特例。为了避免复杂的似然优化，我们结合了伪似然和成对似然方法，并利用多指标部分和的遍历定理，获得了单一路径分析以及面板数据的渐近结果。后一种情形对于分析生态学中物种的存在-缺失数据尤为重要，该领域的数据通常来自不同地点的调查。我们的研究结果为这类常被实践者使用但缺乏概率框架的模型提供了理论基础。