Prévision linéaire des processus à longue mémoire

Abstract : This PhD thesis deals with predicting long-memory processes. We assume that the processes are weakly stationary, linear, causal and invertible, but only a finite subset of the past observations is available.
We first present two approaches when the stochastic structure of the process is known: one is the truncation of the Wiener-Kolmogorov predictor, and the other is the projection of the forecast value on the observations, i.e.\ the least-squares predictor. We show that both predictors converge to the Wiener-Kolmogorov predictor.
When the stochastic structure is not known, we have to estimate the coefficients of the predictors defined in the first part. For the truncated Wiener-Kolomogorov, we use a parametric approach and we plug in the forecast coefficients from the Whittle estimator, which is computed on an independent realisation of the series. For the least-squares predictor, we plug the empirical autocovariances (computed on the same realisation or on an independent realisation) into the Yule-Walker equations. For the two predictors, we estimate the mean-squared error and prove the asymptotic normality.
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Submitted on : Tuesday, December 30, 2008 - 10:50:47 AM
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Fanny Godet. Prévision linéaire des processus à longue mémoire. Mathématiques [math]. Université de Nantes, 2008. Français. ⟨tel-00349384⟩

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