Markov switching autoregressive models for interpreting vertical movement data with application to an endangered marine apex predator

Time series of animal movement obtained from bio-loggers are becoming widely used across all taxa. These data are nowadays of high quality, combining high resolution with precision, as the tags are able to collect for longer times and store larger quantities of data. Due to their nature, high-frequency data sequences often pose non-trivial problems in time series analysis: nonlinearity, non-normality, non-stationarity and long memory. These issues can be tackled by modelling the data sequence as a realization of a stochastic regime-switching process. We suggest a novel Markov switching autoregressive model where the hidden Markov chain is non-homogeneous, with time-varying transition probabilities, whose dynamics depend on the dynamics of some contemporary categorical covariates. To illustrate the use of the method, we apply it to the depth profiles of four individuals of flapper skate (Dipturus cf. intermedia) in order to identify swimming behaviours. Individual time series were obtained from data storage tags that recorded pressure every two minutes. The environmental covariates used were lunar phase (a proxy for the spring-neap tidal cycle), lunar cycle and diel cycle. For all individuals, two states (or regimes) were always selected (the autoregressive order was either three or four), representing different regimes of animal activity, that is state 1 for resting or horizontal swimming or slow vertical movement and state 2 for fast ascending and descending. The cycle of the four lunar phases was the only environmental covariate that explained the hidden state dynamics in all individuals, whereas lunar cycle was selected for two individuals and diel cycle for one only. The method is an efficient approach to fit one-dimensional tag data using categorical environmental covariates, and to classify the observations into a small number of states representing individual behaviours of tagged individuals.