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Bias-Reduced Log-Periodogram And Whittle Estimation Of The Long-Memory Parameter Without Variance Inflation

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  • Guggenberger, Patrik
  • Sun, Yixiao

Abstract

The bias-reduced log-periodogram estimator of Andrews and Guggenberger (2003, Econometrica 71, 675 712) for the long-memory parameter d in a stationary long-memory time series reduces the asymptotic bias of the original log-periodogram estimator of Geweke and Porter-Hudak (1983) by an order of magnitude but inflates the asymptotic variance by a multiplicative constant cr, for example, c1 = 2.25 and c2 = 3.52. In this paper, we introduce a new, computationally attractive estimator by taking a weighted average of estimators over different bandwidths. We show that, for each fixed r 0, the new estimator can be designed to have the same asymptotic bias properties as but its asymptotic variance is changed by a constant cr* that can be chosen to be as small as desired, in particular smaller than cr. The same idea is also applied to the local-polynomial Whittle estimator in Andrews and Sun (2004, Econometrica 72, 569 614) leading to the weighted estimator . We establish the asymptotic bias, variance, and mean-squared error of the weighted estimators and show their asymptotic normality. Furthermore, we introduce a data-dependent adaptive procedure for selecting r and the bandwidth m and show that up to a logarithmic factor, the resulting adaptive weighted estimator achieves the optimal rate of convergence. A Monte Carlo study shows that the adaptive weighted estimator compares very favorably to several other adaptive estimators.We thank a co-editor and three referees for very helpful suggestions. We are grateful for the constructive comments offered by Marc Henry, Javier Hidalgo, and especially Katsumi Shimotsu.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 22 (2006)
Issue (Month): 05 (October)
Pages: 863-912

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Handle: RePEc:cup:etheor:v:22:y:2006:i:05:p:863-912_06

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Cited by:
  1. Arteche, Josu & Orbe, Jesus, 2009. "Using the bootstrap for finite sample confidence intervals of the log periodogram regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1940-1953, April.
  2. Uwe Hassler, 2011. "Estimation of fractional integration under temporal aggregation," Post-Print peer-00815563, HAL.

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