The Finite-Sample Size of the BDS Test for GARCH Standardized Residuals

Abstract

This paper uses a multivariate response surface methodology to analyze the size distortion of the BDS test when applied to standardized residuals of rst-order GARCH processes. The results show that the asymptotic standard normal distribution is an unreliable approximation even in large samples. On the other hand, a simple log-transformation of the squared standardized residuals seems to correct most of the size problems. The estimated response surfaces can nonetheless provide not only a measure of the size distortion, but also more adequate critical values for theBDS test in small samples.