Bias-Reduced Log-Periodogram And Whittle Estimation Of The Long-Memory Parameter Without Variance Inflation
AbstractThe 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 InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 22 (2006)
Issue (Month): 05 (October)
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Other versions of this item:
- Guggenberger, Patrik & Sun, Yixiao, 2004. "Bias-Reduced Log-Periodogram and Whittle Estimation of the Long-Memory Parameter Without Variance Inflation," University of California at San Diego, Economics Working Paper Series qt2z99w4sm, Department of Economics, UC San Diego.
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- 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.
- Uwe Hassler, 2011.
"Estimation of fractional integration under temporal aggregation,"
- Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
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