Periodic Markov switching autoregressive models for Bayesian analysis and forecasting of air pollution

Markov switching autoregressive models (MSARMs) are efficient tools to analyse nonlinear and non-Gaussian time series. A special MSARM with two harmonic components is proposed to analyse periodic time series. We present a full Bayesian analysis based on a Gibbs sampling algorithm for model choice and the estimations of the unknown parameters, missing data and predictive distributions. The implementation and modelling steps are developed by tackling the problem of the hidden states labeling by means of random permutation sampling and constrained permutation sampling. We apply MSARMs to study a data set about air pollution that presents periodicities since the hourly mean concentration of carbon monoxide varies according to the dynamics of the 24 day-hours and of the year. Hence, we introduce in the model both a hidden state-dependent daily component and a state-independent yearly component, giving rise to periodic MSARMs.