Comparison of the GARCH and stochastic models: An application to the Mexican peso-us dollar exchange rate

Resumen

Forecasting volatility is of great importance an important topic for researchers, entrepreneurs, and policymakers. This work compares different volatility models to ascertain their forecasting efficiency. The models include standard approaches such as Autoregressive Conditional Heteroskedasticity (GARCH), exponential GARCH, and Stochastic Volatility models (SV). For estimation, a comparison between the Frequentist and the Bayesian approaches are made using the maximum likelihood and the Monte Carlo Markov Chains (MCMC) methods. The case analysis considers the Mexican peso/US dollar exchange
rate. The results show a favorable behavior between the SV models estimated with the MCMC and the GARCH models in forecasting out of the sample. Additionally, the analysis shows that the current volatility reacts to the data within the last period, despite the former periods.