On testing the adequacy of stable processes under conditional heteroscedasticity

Abstract

We consider a recently proposed method of estimating the tail index and testing the goodness-of-fit of dependent stable processes. Through Monte Carlo simulations, we evaluate the ability of the procedure to distinguish between stable and non-stable processes in 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 distributional and tail behaviour has been analysed previously in the literature. After adjusting for seasonality, we conclude, unlike the earlier analysis, that a stable process cannot be rejected as a model for some of the currencies. Estimates of the tail index for these currencies are also obtained.