Theory and inference for multivariate autoregressive binary models with an application to absence-presence data in ecology

TL;DR

This paper develops a theoretical framework and inference methods for multivariate autoregressive binary models, with applications to ecological data on species presence-absence, combining pseudo-likelihood approaches and establishing asymptotic properties.

Contribution

It introduces a general class of autoregressive models for binary time series with exogenous covariates and provides a probabilistic foundation and inference techniques, especially for ecological presence-absence data.

Findings

Existence of stationary paths is almost automatic under broad conditions.

Pseudo-likelihood and pairwise likelihood methods are effective for inference.

Asymptotic results are established for single and panel data scenarios.

Abstract

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.