A Bayesian approach to model changes in volatility in the Mexican stock exchange index

We model the changes in volatility in the Mexican Stock Exchange Index using a Bayesian approach. We study the time series with a wide set of models characterized by a Markov switching heterogeneity. The advantage of this approach is that it allows for a broader spectrum of possible models since the estimation of the moments of the parameters is done using the finite mixture distribution MCMC method, without relying on assumptions about large sampling and mathematical optimization. This is particularly relevant for emerging markets' financial data because of its special characteristics, like being more susceptible to jumps and changes in volatility caused by exchange rate swings, financial crises and oil and commodity prices. For model comparison, we use the marginal likelihood approach and the bridge sampling technique. The best representation of the data is given by a switching model with three states rather than any other autoregressive linear or non-linear model. The periods of volatility found by the model coincide with different financial crisis. Whereas other studies of volatility for the same market impose the Markovian model that captures changes in volatility, we let our model to be defined in an endogenous way.