A non-nested test of GARCH vs. EGARCH models

Abstract

This study uses a Cox-type non-nested test. The test is obtained using Monte Carlo hypothesis tests with the log likelihood ratio as the test statistic. Monte Carlo methods are used to obtain the probability of a larger value of the test statistic under the null hypothesis. The approach used does not rely upon asymptotic normality. Using the maximum likelihood estimation technique, two competing time series models, generalized autoregressive conditional heteroscedasticity (GARCH) and exponential GARCH (EGARCH) models of daily spot prices of Deutsche mark are estimated. Using Monte Carlo hypothesis tests, then, p-values for GARCH vs. EGARCH models are calculated. The EGARCH model cannot be rejected, while the GARCH model is rejected.