Although the properties of the ARCH(∞) model are well investigated, the existence of long memory FIGARCH and IARCH solution was not established in the literature. These two popular ARCH type models which are widely used in applied literature, were causing theoretical controversy because of the...

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, st. Stationary solution of (*) is obtained as an orthogonal Volterra expansion. In the case...

This paper discusses asymptotic normality of certain classes of M- and R-estimators of the slope parameter vector in linear regression models with long memory moving average errors, extending recent results of Koul (1992) and Koul and Mukherjee (1993). Like in the case of the long memory...