ESTIMATION FOR THE STATIONARY MULTIVARIATE LONG MEMORY LINEAR PROCESS

In this note, we consider in R-m the linear process ((X) under bar (t))(r is an element of Z) which is defined as (X) under bar (t) = Sigma(infinity)(u=0) psi(u)(theta)(Z) under bar (t-u) where ((Z) under bar)(t is an element of Z) is a sequence of strictly stationary m-dimensional associated random vectors, independent and identically distributed. {Psi(u)} is a square-summable sequence of (m x m)- matrix in the sense that Sigma(infinity)(u=0) psi psi' < infinity. Moreover, we assume that E(<(Z)under bar>(t)) = 0 and E((Z) under bar (t)(Z) under bar'(t)) = Sigma > 0. theta is an element of Theta a compact subset of R-q. The process is assumed to be a Gaussian and long memory process. We construct the minimum Hellinger distance estimator of the parameters of the stationary multivariate long memory linear process. This method is based on the minimization of the Hellinger distance between the random function of (X) under bar (k) and a theoretical probability density f(theta)(.). We establish, under some assumptions, the almost sure convergence of the estimator and its asymptotic normality.