Test for tail index constancy of GARCH innovations based on conditional volatility

Abstract

This study considers the problem of testing whether the tail index of the GARCH innovations undergoes a change according to the values of conditional volatilities. Special attention is paid to power-transformed and threshold generalized autoregressive conditional heteroscedasticity processes that can accommodate the GARCH family. We show that the proposed test asymptotically follows a functional of a standard Brownian motion under some regularity conditions. To evaluate our method, we carry out a simulation study and real data analysis using the return series of the Google stock price and DowJones index.