Linear Prediction of Long-Memory Processes: Asymptotic Results on Mean-squared Errors

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 $k$ terms, which are the only available values in practice. We derive the asymptotic behaviour of the mean-squared error as $k$ tends to $ + \infty$. By contrast, the second approach is non-parametric. An AR($k$) model is fitted to the long-memory time series and we study the error that arises in this misspecified model.

Domaines: Statistiques [math.ST]

Fanny Godet. Linear Prediction of Long-Memory Processes: Asymptotic Results on Mean-squared Errors. 2007. ⟨hal-00146246⟩