arXiv subjects

Guillaume Franchi

Publications and source records attributed to Guillaume Franchi.

2 recordsLinked to original sources

arXiv2024

Time series on compact spaces, with an application to dynamic modeling of relative abundance data in Ecology

Motivated by the dynamic modeling of relative abundance data in ecology, we introduce a general approach to model stationary Markovian or non Markovian time series on (relatively) compact spaces such as a hypercube, the simplex or a sphere in the Euclidean space. Our approach is based on a general construction of infinite memory models, called chains with complete connections. The two main ingredients involved in our generic construction are a parametric family of probability distributions on the state space and a map from the state space to the parameter space. Our framework encompasses Markovian models, observation-driven models and more general infinite memory models. Simple conditions ensuring the existence and uniqueness of a stationary and ergodic path are given. We then study in more details statistical inference in two time series models on the simplex, based on either a Dirichlet or a multivariate logistic-normal conditional distribution. Usefulness of our models to analyze abundance data in ecosystems is also discussed.

math.ST↗

arXiv2024

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

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.

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