For a particular conditionally heteroscedastic nonlinear (ARCH) process for
which the conditional variance of the observable sequence r(t) is the squa
re of an inhomogeneous linear combination of r(s), s < t, we give condition
s under which, for integers l <greater than or equal to> 2, r(t)(l) has lon
g memory autocorrelation and normalized partial sums of r(t)(l) converge to
fractional Brownian motion.