The BDS test as a test for the adequacy of a GARCH(1,1) specification: a Monte Carlo study

In this study we examine the widely used Brock, Dechert and Scheinkman (BDS) test when applied to the logarithm of the standardized residuals of an estimated GARCH(1,1) model as a test for the adequacy of this speci?cation. We review the conditions derived by De Lima (1996, Econometric Reviews, 15, 237-259) for the nuisance-parameter free property to hold, and address the issue of their necessity, using the ?exible framework offered by the GARCH(1,1) model in terms of moment, memory and time heterogeneity properties. By means of Monte Carlo simulations, we show that the BDS test statistic still approximates the standard null distribution even for mildly explosive processes that violate the majority of the conditions. Thus, the test performs reasonably well, its empirical size being rather close to the nominal one. As a by-product of this study, we also shed light on the related issue of consistency of the QML estimators of the conditional variance parameters under various parameter con?gurations and alternative distributional assumptions on the innovation process.