2024/07/14 by Guillaume Franchi, Franchi, Guillaume, Lionel Truquet +1
Agricultural and Biological Sciences · Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Sensory Analysis and Statistical Methods #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2407.10260
openalex publication_date 2024/07/14 · openalex created_date 2024/07/17 · openalex updated_date 2026/07/28
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.