Modeling and Projection of the Mexican Exchange Rate (Peso/Dollar): a Bayesian Approach for Model Selection

Abstract

This article studies the econometric modeling and the projection of growth rates of the nominal exchange rate (Peso/Dollar) from 1995 to 2018. Applying Bayesian simulation methods, the best data modeling fit between linear and non-linear econometric approaches is studied by introducing Markovian regime change parameters. The Bayes factor for model selection provides the following evidence: in the analysis of daily growth rates there are periods with low, medium, and high volatility. In the monthly rates, changes were also found in the mean and the volatility of the process. The linear autoregressive econometric model is not supported by the data in any case. Furthermore, instead of structural changes in these rates, evidence of state-dependent parameters is present. The high volatility in both data frequencies coincides with the sub-prime crisis in 2008-2009, but also with other sample periods. Moreover, an optimal weighting approach is applied to Markovian regime change models to study forecast errors in the sample. From this exercise, the forecasting errors of the exchange rate growth rates are lower than those of the linear autoregressive model. Finally, the out-of-sample errors of regime change models and optimal methods, in most cases, exceed those of linear inferences in both data frequencies.