Test for tail index constancy of GARCH innovations based on conditional volatility (Q2317888)

The authors consider power-transformed and threshold GARCH models. Interactions between the tail index of innovation distribution and the value of conditional volatility of processes are investigated. The problem is studied by using the framework of a change point analysis. The paper designs a residual-based test to check the constancy of the tail index over the values of conditional volatilities. It is shown that under regularity conditions the test asymptotically follows a functional of a standard Brownian motion. Simulation studies and real data analysis of the Google stock price and DowJones index are provided.