Linear prediction of long-range dependent time series

Laboratoire de Mathématiques Jean Leray, UMR CNRS 6629, Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France; fanny.godet@math.univ-nantes.fr

Received: 11 May 2007
Revised: 31 December 2007

Abstract

We present two approaches for linear prediction of long-memory time series. The first approach consists in truncating the Wiener-Kolmogorov predictor by restricting the observations to the last k terms, which are the only available data in practice. We derive the asymptotic behaviour of the mean-squared error as k tends to +∞. The second predictor is the finite linear least-squares predictor i.e.  the projection of the forecast value on the last k observations. It is shown that these two predictors converge to the Wiener Kolmogorov predictor at the same rate k^-1.