Prediction of long memory processes on same-realisation

Fanny Godet (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

Let observations come from an infinite autoregressive long memory process. For predicting the future values, we use the least-squares predictor where the forecast coefficients are estimated on the same realisation. The aim of this paper is to express the rate of convergence of this predictor as the number of observations goes to infinity. We generalise the results of Ing and Wei for short memory processes. We first have to prove sharp moment bound for the inverse empirical covariance matrix. We then obtain an asymptotic expression of the mean-squared prediction error of this predictor. The second order term of this expression is the sum of two terms: the first corresponds to the complexity of the predictor and the second to goodness of fit of the theoretical predictor. Finally we prove a central limit theorem for this predictor.

Domaines: Statistiques [math.ST]

Fanny Godet. Prediction of long memory processes on same-realisation. 2007. ⟨hal-00196208v1⟩