A Model Specification Test For GARCH(1,1) Processes

摘要

We provide a consistent specification test for generalized autoregressive conditional heteroscedastic (GARCH(1,1)) models based on a test statistic of Cramer-von Mises type. Because the limit distribution of the test statistic under the null hypothesis depends on unknown quantities in a complicated manner, we propose a model-based (semiparametric) bootstrap method to approximate critical values of the test and to verify its asymptotic validity. Finally, we illuminate the finite sample behaviour of the test by some simulations.