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Log-periodogram regression on non-Fourier frequencies sets| old_uid | 7463 |
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| title | Log-periodogram regression on non-Fourier frequencies sets |
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| start_date | 2009/10/16 |
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| schedule | 11h |
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| online | no |
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| summary | 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". |
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| responsibles | Bardet, Cottrell |
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