Volume 13, January 2009
|Page(s)||115 - 134|
|Published online||26 March 2009|
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; firstname.lastname@example.org
Revised: 31 December 2007
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.
Mathematics Subject Classification: 62M20 / 62M10
Key words: Long-memory / linear model / autoregressive process / forecast error
© EDP Sciences, SMAI, 2009
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