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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

In this paper, we introduce a new, computationally attractive estimator of long memory by taking a weighted average of the GPH or local Whittle estimator over different bandwidths. We show that the new estimator can be designed to have the same asymptotic bias properties as the bias-reduced estimators of Andrews and Guggenberger (2003) or Andrews and Sun (2004) but its asymptotic variance is smaller than that of the latter estimators. 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, the number of bias terms to be eliminated, 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.

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Bibliographic Info

Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt2z99w4sm.

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Date of creation: 01 Nov 2004
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Handle: RePEc:cdl:ucsdec:qt2z99w4sm

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Related research

Keywords: Adaptive Estimation; Asymptotic Bias; Asymptotic Normality; Bias Reduction; Frequency Domain; Long-Range Dependence; Rate of Convergence;

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Cited by:
  1. Uwe Hassler, 2011. "Estimation of fractional integration under temporal aggregation," Post-Print hal-00815563, HAL.
  2. 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.
  3. 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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