Evaluating GARCH models

In this paper, a unified framework for testing the adequacy of an estimated GARCH model is presented. Parametric Lagrange multiplier (LM) or LM type tests of no ARCH in standardized errors, linearity, and parameter constancy are proposed. The asymptotic null distributions of the tests are standard, which makes application easy. Versions of the tests that are robust against nonnormal errors are provided. The finite sample properties of the test statistics are investigated by simulation. The robust tests prove superior to the nonrobust ones when the errors are nonnormal. They also compare favourably in terms of power with misspecification tests previously proposed in the literature.