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09 - Log-periodogram regression on non-Fourier frequencies sets (Mohamed Boutahar (GREQAM, Université de Marseille-Luminy))

16 octobre 2009
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Résumé : In the log-periodogram regression, the Fourier frequencies lambda_{j,n} = 2 pi j/n are used to define the estimator of the long memory parameter d. Moreover the number of frequencies m considered depends on the sample size n through the condition 1/m + m/n -> 0 as n ->infty. However, a rigorous asymptotic semiparametric theory to give a satisfactory choice for m is still lacking. The main objective of this paper is to fill this gap. We define a non-Fourier logperiodogram estimator by performing an OLS regression, in which non-Fourier frequencies independent of the sample size n are used. We show that this new estimator is consistent and asymptotically normal if n -> infty and m -> infty without imposing the rate condition m/n -> 0. Based on the rate of convergence in the Central Limit Theorem, a moderate m, m = 30 say, is sufficient to obtain a reliable confidence interval for d. <!-- Fin de l'affichage de l'article --> <!-- A lire dans la meme rubrique -->

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