A model for long memory conditional heteroscedasticity

Abstract

For a particular conditionally heteroscedastic nonlinear (ARCH) process for which the conditional variance of the observable sequence rt is the square of an inhomogeneous linear combination of rs, s < t, we give conditions under which, for integers l ≥ 2, rlt has long memory autocorrelation and normalized partial sums of rlt converge to fractional Brownian motion.