A mixed portmanteau test for ARMA-GARCH models by the quasi-maximum exponential likelihood estimation approach

This paper investigates the joint limiting distribution of the residual autocorrelation functions and the absolute residual autocorrelation functions of ARMA-GARCH models. This leads a mixed portmanteau test for diagnostic checking of the ARMA-GARCH model fitted by using the quasi-maximum exponential likelihood estimation approach in Zhu and Ling (2011). Simulation studies are carried out to examine our asymptotic theory, and assess the performance of this mixed test and other two portmanteau tests in Li and Li (2008). A real example is given.