Empirical likelihood test for the application of swqmele in fitting an arma-garch model

Fitting an ARMA-GARCH model has become a common practice in financial econometrics. Because the asymptotic normality of the quasi maximum likelihood estimation (QMLE) requires finite fourth moment for both errors and the sequence itself, self-weighted quasi maximum exponential likelihood estimation (SWQMELE) has been proposed to reduce the moment constraints but requires the errors to have zero median instead of zero mean. Because changing zero mean to zero median destroys the ARMA-GARCH structure and has a serious effect on skewed data, this article proposes an efficient empirical likelihood test for zero mean of errors in the application of SWQMELE to ensure that the model still concerns conditional mean. A simulation study confirms the good finite sample performance before applying the test to the US housing price indexes and financial returns for the study of comovement.

Automated summary

This paper discusses the use of the ARMA-GARCH model in financial econometrics and proposes an empirical likelihood test to address zero mean errors when using the SWQMELE method. Simulation studies confirm the effectiveness of this test before applying it to empirical research.