Maximum likelihood estimation of bivariate circular hidden Markov models from incomplete data

In this paper, we propose a hidden Markov model for the analysis of the time series of bivariate circular observations, by assuming that the data are sampled from bivariate circular densities, whose parameters are driven by the evolution of a latent Markov chain. The model segments the data by accounting for redundancies due to correlations along time and across variables. A computationally feasible expectation maximization (EM) algorithm is provided for the maximum likelihood estimation of the model from incomplete data, by treating the missing values and the states of the latent chain as two different sources of incomplete information. Importance-sampling methods facilitate the computation of bootstrap standard errors of the estimates. The methodology is illustrated on a bivariate time series of wind and wave directions and compared with popular segmentation models for bivariate circular data, which ignore correlations across variables and/or along time.