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

2023/02/01 by Franchi, Guillaume, Truquet, Lionel
#Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2302.00519

Abstract

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.

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