Linear Prediction of Long-Range Dependent Time Series

Fanny Godet (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

We present two approaches for next step linear prediction of long memory time series. The first is based on the truncation of the Wiener-Kolmogorov predictor by restricting the observations to the last $k$ terms, which are the only available values in practice. Part of the mean squared prediction error comes from the truncation, and another part comes from the parametric estimation of the parameters of the predictor. By contrast, the second approach is non-parametric. An AR($k$) model is fitted to the long memory time series and we study the error made with this misspecified model.

Mots clés: Long memory; linear model; autoregressive process; forecast error

Domaines: Statistiques [math.ST]

Fanny Godet. Linear Prediction of Long-Range Dependent Time Series. ESAIM: Probability and Statistics, 2009, 13, pp.115-134. ⟨hal-00131530v2⟩