A New Class of Characteristic-Function-Based Distribution Tests and Its Application to GARCH Model

This paper proposes a new class of characteristic-function-based distribution tests for two-sample comparison, simple hypotheses, and conditional distribution assumptions of econometric models. The proposed tests are easy to compute and have χ2(2) as the asymptotic null distribution. Comparing to the Kolmogorov-Smirnov (KS) and Cramérvon Mises (CV) tests, the proposed test can flexibly account for the difference between the true and postulated distributions at different frequencies. A Monte Carlo simulation study shows that the proposed test significantly outperforms the KS, CV, and Pearson’s χ2 tests, especially when the true and postulated distributions are both symmetric. In an empirical study of stock index returns, we apply the proposed test to check distribution assumptions of the standardized errors of GARCH(1,1) model, including the standard normal, standardized t, logistic, generalized error, and generalized lambda distributions. The proposed test accepts the standardized t distribution but rejects the standard normal distribution for all the returns considered; the appropriateness of other distribution assumptions are data-specific. This empirical study also shows that the conditional normality assumption may render the GARCH(1,1) model over-estimating the impact effect of external shocks on volatility but under-estimating the persistence of these shocks’ influences, especially when the markets are volatile. JEL classification: C12, C22, C52, G19