Evaluating GARCH Models

This paper suggests a unified framework for testing the adequacy of anestimated GARCH model. Nothing more complicated than standard asymptotictheory is required. Parametric tests of no ARCH in standardized errors,symmetry, and parameter constancy are suggested. Estimating the alternativewhen the null hypothesis is rejected may give useful ideas of how to improvethe specification. It is also shown that the recent portmanteau test of Liand Mak (1994) is asymptotically equivalent to our test of no ARCH in thestandardized error process.