On Testing the Adequacy of Stable Processes Under Conditional Heteroscedasticity

Abstract

We consider a recently proposed method of estimating the tail index and testing thegoodness-of-fit of dependent stable processes. Through Monte Carlo simulations, weevaluate the ability of the procedure to distinguish between stable and non-stable processesin the presence of non-linear dependence and to estimate the tail index of the distribution.We then apply the test to black market East European exchange rates, whose distributionaland tail behaviour has been analysed previously in the literature. After adjusting forseasonality, we conclude, unlike the earlier analysis, that a stable process cannot be rejectedas a model for some of the currencies. Estimates of the tail index for these currencies arealso obtained.

Keywords: Stable, Goodness-of-fit, Conditional heteroscedasticity, Tail index