A hidden Markov model for the analysis of cylindrical time series

Abstract

A new hidden Markov model is proposed for the analysis of cylindrical time series, that is, bivariate time series of intensities and angles. It allows us 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. Copyright © 2015 John Wiley & Sons, Ltd.