A model for long memory conditional heteroscedasticity. (Q1872488)

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