B0771
Title: Segmenting toroidal time series by non-homogeneous hidden semi-Markov models
Authors: Francesco Lagona - University Roma Tre (Italy) [presenting]
Marco Mingione - University of Roma Tre (Italy)
Abstract: Bivariate sequences of angles are often referred to as toroidal time series because the pair of two angles can be represented as a point on a torus. Examples include time series of wind and wave directions and time series of turning angles in studies of animal movement. A nonhomogeneous, toroidal hidden semi-Markov model (HSMM) is introduced that segments toroidal time series. Precisely, the distribution of toroidal data is approximated by a mixture of toroidal densities, whose parameters evolve according to a latent semi-Markov process with covariate-specific dwell times. The proposal extends previous approaches that are based on toroidal hidden Markov models. Under a toroidal hidden Markov model, the sojourn times of the states of the latent process are distributed according to a geometric distribution. The proposal relaxes this restrictive assumption by replacing the latent Markov chain with a latent, nonhomogeneous semi-Markov model, where the (not necessarily geometric) time spent in a given regime and the chances of a regime-switching event are separately modelled by a battery of regression models that allow the introduction of covariates. Parameter estimates are computed by an EM algorithm that alternates the maximization of a complete-data log-likelihood function that relies on weighed augmented data with weights updating. The proposal is finally illustrated on a time series of wind and wave directions observed in the Adriatic Sea.
