Estimation of Garch Models for Nigerian Exchange Rates Under Non-Gaussian Innovations

Abstract

Financial series often displays evidence of leptokurticity and in that case, the empirical distribution often fails normality.  GARCH models were initially based on normality assumption but estimated model based on this assumption cannot capture all the degree of leptokurticity in the return series. In this paper, we applied variants of GARCH models under non-normal innovations-t-distribution and Generalized Error Distribution (GED) on selected Nigeria exchange rates. The Berndt, Hall, Hall, Hausman (BHHH) numerical derivatives applied in the estimation of models converged faster and the time varied significantly across models. Asymmetric GARCH model with t-distribution (GARCH-t) was selected in most of the cases whereas for Nigeria-US Dollar exchange rate, GARCH-GED was specified. Both distributions showed evidence of leptokurticity in Naira exchange rate return series. The result is of practical importance to practitioners.

Key Words: GARCH, Exchange rate, Model specification, Non-Gaussian distribution.