A Copula-Based Hidden Markov Model for Toroidal Time Series

Toroidal time series are temporal sequences of bivariate angular observations that often arise in environmental and ecological studies. A hidden Markov model is proposed for segmenting these data according to a finite number of latent classes, associated with copula-based toroidal densities. The model conveniently integrates circular correlation, multimodality and temporal auto-correlation. A computationally efficient EM algorithm is proposed for parameter estimation. The proposal is illustrated on a time series of wind and sea wave directions.