Auto-tail Dependence Coefficients for Stationary Solutions of Linear Stochastic Recurrence Equations and for GARCH(1,1)

Abstract

We examine the auto-dependence structure of strictly stationary solutions of linear stochastic recurrence equations and of strictly stationary GARCH(1, 1) processes from the point of view of ordinary and generalized tail dependence coefficients. Since such processes can easily be of infinite variance, a substitute for the usual auto-correlation function is needed.