Hidden chain reconstruction, missing observation restoration, multi-step forecasting by means of Markov switching autoregressive models

We consider Markov switching autoregressive models to tackle the prediction problem of nonlinear time series with missing data. We obtain the maximum likelihood estimators of the parameters of the model by the EM algorithm and we reconstruct the sequence of the hidden states by a Monte Carlo procedure. Then we restore the missing observations and forecast the future values of the observed variable through a new multistep forecasting procedure based on the reconstructed chain. This method is applied to analyse a time series of daily mean concentrations of sulphur dioxide; the different levels of the pollution are described by the dynamics of the hidden states.