Robust tests for ARCH and GARCH components

Abstract

Two robust one-sided tests are proposed for detecting ARCH and GARCH components. The first one is distribution free being a rank test based on the van der Waerden scores. The related test statistic has mean and variance known in closed form; moreover, it is shown to be asymptotically normal and its finite sample critical values have been estimated via the Monte Carlo method. The second test is the one sided modification of the Gregory test which is of course more powerful than the corresponding original two sided version. An extensive Monte Carlo analysis has been performed and - as long as it is generalizable - the following conclusions can be drawn. The new rank test performs well both for ARCH observations and ARCH residuals. From robustness point of view, under the null hypothesis, some bias appears for ARCH residuals from heavily asymmetric distributions. In this case the modified Gregory test is recommended. In the other situations i.e. ARCH observations from symmetric or asymmetric distributions and ARCH residuals from symmetric distributions the rank test is shown to be robust under the null hypothesis and more powerful with respect to the modified Gregory test. The rank test can be recommended as a useful alternative to the standard Lee and King test, which is the reference test for normal observations. As a matter of fact, it seems more robust under the null hypothesis and more powerful for non normal distributions. For normal distributions neither of these two dominates the other.