Modeling the Volatility of Exchange Rate Returns

This paper focuses on modeling the evolution of volatility deterministically through (G)ARCH models and compares the performance of the different models, using the daily bilateral prices of one USD to 1 Euro from January 04, 1999 until June 23, 2017. It also compares the performance of these models vis-a-vis an extension of (G)ARCH models that can be obtained by allowing for t-distribution errors. It uses the maximum likelihood technique to specify the degrees of freedom parameter for the t-distribution; hence, determining the maximum likelihood estimate of the t-distribution degrees of freedom, while fixing the AR(q) model for the mean process. It shows that adjusting the AR(q) - GARCH(1,1) model to assume t-distribution for the residuals improve the fit of model.