A Simple Portmanteau Test For Weak GARCH Models

Models for time series are quite popular in Economics,Finance,Statistics and Econometrics and GARCH models are usually used to study the volatility in financial market.However,people sometimes would ignore the important assumptions when using the models,which is likely to have an inverse effect on modelling.For example,the Portmanteau test follows a chi squared distribution,under the assumption that the residuals are independent.As a result,it is important to relax the strict assumptions.In this paper,we follow the idea of Wang,who proposed a simple portmanteau test for ARMA models with weak innovations in 2016.This portmanteau test is useful for weak models because of an innovative transform of the sample autocorrelations of residuals,which allows for the weak innovations and parameters estimation effect.It can be regarded as an extension of Box and Pierce's Q test.We rewrite the specification of weak GARCH models and show the simple portmanteau test is also effective in this case.Monto Carlo simulations also show that by using the Newey-West approach,the simple portmanteau test enjoys good size and not bad power.An application to the daily returns CSI 300 Index illustrates the merits of the testing procedure.