We consider a simple bilinear process X-t = aX(t-1) + bX(t-1)Z(t-1) +Z(t),
where (Z(t)) is a sequence of iid N(0, 1) random variables. It follows from
a result by Kesten (1973, Acta Math. 131, 207-248) that X-t has a distribu
tion with regularly varying tails of index alpha > 0 provided the equation
E\a + bZ(1)\(u) = 1 has the solution u = alpha. We study the limit behaviou
r of the sample autocorrelations and autocovariances of this heavy-tailed n
on-linear process. Of particular interest is the case when alpha < 4. If al
pha is an element of (0,2) we prove that the sample autocorrelations conver
ge to non-degenerate limits. If alpha is an element of (2,4) we prove joint
weak convergence of the sample autocorrelations and autocovariances to non
-normal limits. (C) 1999 Elsevier Science B.V. All rights reserved.