Our data set is composed of monthly observations. The use of monthly data is due to the fact that many macroeconomic data used as explanatory variables for the time varying Markov probabilities, are available only at monthly frequencies. However, nominal exchange rate data is also available at daily frequencies. For each month and for each exchange rate analyzed we selected the highest (log) price and the lowest (log) price to compute the monthly range (see Chou, 2005). Therefore, the time interval 0 n N in our set up corresponds to a month. Finally, the volatility (standard deviation) proxy is computed as