Maximum Likelihood Approach to Markov Switching Models

The present paper concerns a Maximum Likelihood analysis for the Markov switching approach to the forecasting problem of financial time series. In particular we model the volatility parameter characterizing time series of interest as a state variable of a suitable Markov chain. Latter formulation is based on the idea of describing abrupt changes in the behaviour of studied financial quantities due to, e.g., social or political factors able to substantially change the economic scenarios we are interested in. A case study for the NASDAQ IXIC index in the period 3rd Jan 2007 - 30th Dec 2013 is also provided.