A Hidden Markov model for the analysis of cylindrical time series

A new hidden Markov model is proposed for the analysis of cylindrical time series, i.e. bivariate time series of intensities and angles. It allows to segment cylindrical time series according to a finite number of regimes that represent the conditional distributions of the data under specific environmental conditions. The model parsimoniously accommodates for circular-linear correlation, multimodality, skewness and temporal autocorrelation. A computationally efficient Expectation-Maximization algorithm is described to estimate the parameters and a parametric bootstrap routine is provided to compute confidence intervals. These methods are illustrated on cylindrical time series of wave heights and directions.