We discuss the covariance structure and long-memory properties of stationary solutions of the bilinear equation Xt=[zeta]tAt+Bt,(*), where are standard i.i.d. r.v.'s, and At,Bt are moving averages in Xs, s<t. Stationary solution of (*) is obtained as an orthogonal Volterra expansion. In the case At[reverse not equivalent]1, Xt is the classical AR([infinity]) process, while Bt[reverse not equivalent]0 gives the LARCH model studied by Giraitis et al. (Ann. Appl. Probab. 10 (2000) 1002). In the general case, Xt may exhibit long memory both in conditional mean and in conditional variance, with arbitrary fractional parameters and , respectively. We also discuss the hyperbolic decay of auto- and/or cross-covariances of Xt and Xt2 and the asymptotic distribution of the corresponding partial sums' processes.
