Estimation of Markovian-regime-switching models with independent regimes

Markovian-regime-switching (MRS) models are commonly used for modelling economic time series, including electricity prices where independent regime models are used, since they can more accurately and succinctly capture electricity price dynamics than dependent regime MRS models can. We can think of these independent regime MRS models for electricity prices as a collection of independent AR(1) processes, of which only one process is observed at each time; which is observed is determined by a (hidden) Markov chain. Here we develop novel, computationally feasible methods for MRS models with independent regimes including forward, backward and EM algorithms. The key idea is to augment the hidden process with a counter which records the time since the hidden Markov chain last visited each state that corresponding to an AR(1) process.