Evaluating GARCH Models

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