Markov switching models for high-frequency time series from automatic monitoring of animals

Speaker: Luigi Spezia (BIOSS, James Hutton Institute)

Abstract

In ecological studies data loggers can be applied to mammals, fishes, and birds to automatically monitor the movements of animals to study their behaviour. Sensors applied to animals generate high-frequency complex time series that are modelled along with environmental dynamic variables. Animal movement time series usually exhibit high autocorrelations at the higher lags, with a slow decay, and asymmetric cycles. Both issues suggest to handle the series as realizations of a stochastic regime switching process. Hence, Markov switching autoregressive models (MSARMs) can be considered. Covariates can also be incorporated into the model through the hidden Markov chain: the transition probabilities are time-varying and dependent on dynamic explanatory variables.

Our modelling is motivated by a real application: the time series of depth profiles recorded by Data Storage Tags applied to flapper skates (Dipturus intermedia) caught in the Sound of Jura (Scotland) in 2012. Inference is developed under the Bayesian paradigm by Markov chain Monte Carlo (MCMC) algorithms. We demonstrate that MSARMs are very good tools to fit the long memory, non-linear, non-Normal, non-stationary processes of depth profiles, and to cluster the observations into regimes of movement. New methodological contributions have been also developed: i) the hidden Markov chain is assumed to be non-homogeneous, with multiple transition matrices alternating according to the dynamics of some categorical covariates; ii) the identifiability of the model is solved without placing any constraint, but by an automatic reordering of the draws obtained at each sweep of the MCMC algorithm.

This is joint work with Cecilia Pinto, Laboratoire Ressources Halieutiques de Boulogne, Ifremer, Boulogne-sur-Mer, France.