State space Markov switching models using wavelets

We propose a state space model with Markov switching, whose regimes are associated with the model parameters and regime transition probabilities are modeled using wavelets. The estimation is based on the maximum likelihood method using the EM algorithm and a bootstrap method is proposed in order to assess the distribution of the maximum likelihood estimators. To evaluate the state variables and regime probabilities, the Kalman filter and a probability filter procedure conditional on each possible regime, at each instant, are used. These procedures are evaluated with simulated data and illustrated with the US monthly industrial production index from July 1968 to February 2011.