Markov switching time series models with application to a daily runoff series

We consider a class of Bayesian dynamic models that involve switching among various regimes. As an example we produce a model for a runoff time series exhibiting pulsatile behavior. This model is a mixture of three autoregressive models which accommodate "rising," "falling," and "normal" states in the runoff process. The mechanism for switching among regimes is given by a three state Markov chain whose transition probabilities are modeled on the basis both of past runoff values and of a time series of rainfall data. We adopt the Bayesian approach and use the Gibbs sampler in the numerical analyses. A study of a daily runoff series from Lake Taupo, New Zealand, is given.