Estimation of a stationary multivariate ARFIMA process

Abstract

In this note, we consider an m-dimensional stationary multivariate long memory ARFIMA (AutoRegressive Fractionally Integrated Moving Average) process, which is defined as : A ( L ) D ( L ) ( y 1 ( t ),..., y m ( t ))' = B ( L ) ( ∈ 1 ( t ),..., ∈ m ( t ))', where M ' denotes the transpose of the matrix M . We determine the minimum Hellinger distance estimator (MHDE) of the parameters of a stationary multivariate long memory ARFIMA. This method is based on the minimization of the Hellinger distance between the random function of f n (.) and a theoretical probability density f θ (.). We establish, under some assumptions, the almost sure convergence of the estimator and its asymptotic normality. Keywords: Stationary Multivariate ARFIMA process; Estimation; Long memory; Minimum Hellinger distance AMS 2010 Mathematics Subject Classification: 62F12, 62H12