In this paper we study a possible synchronization in volatility changes for some Latin America's stock exchange indexes. We also add the S&P 500 index to the analysis. We suggest a heterogeneity Markov switching model to capture changes in volatilities over time.To solve the problem of uncertainty in modeling each index, we suggest the Bayes Factor to identify the best Markov switching specification as the number of states, if any. We found that, all the daily growth rates for each index are well characterized by low, medium and high volatilities in different periods of time. We suggest some measures of synchronization based on the concordance by the changes in volatilities between the indexes. We show that, the Mexican, Chilean and the S&P 500 indexes are closer to each other than the rest
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