Linear prediction of long-range dependent time series

Fanny Godet (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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 terms, which are the only available data in practice. We derive the asymptotic behaviour of the mean-squared error as tends to . The second predictor is the finite linear least-squares predictor  the projection of the forecast value on the last observations. It is shown that these two predictors converge to the Wiener Kolmogorov predictor at the same rate .

Mots clés: Mathematics

Fanny Godet. Linear prediction of long-range dependent time series. ESAIM: Probability and Statistics, 2009, 13, pp.115-134. ⟨10.1051/ps:2008015⟩. ⟨hal-00480193⟩