Gibbs sampling approach to regime switching analysis of financial time series

We will introduce a Monte Carlo type inference in the framework of Markov Switching models to analyse financial time series, namely the Gibbs Sampling. In particular we generalize the results obtained in Albert and Chib (1993), Di Persio and Vettori (2014) and Kim and Nelson (1999) to take into account the switching mean as well as the switching variance case. In particular the volatility of the relevant time series will be treated as a state variable in order to describe the abrupt changes in the behaviour of financial time series which can be implied, e.g., by social, political or economic factors. The accuracy of the proposed analysis will be tested considering financial dataset related to the U.S. stock market in the period 2007–2014.