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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.

Suggested Citation

  • 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.
    • Handle: RePEc:cdl:ucsdec:qt2z99w4sm
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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. Saeed Heravi & Kerry Patterson, 2013. "Log-Periodogram Estimation of the Long-Memory Parameter: An Evaluation of Competing Estimators," Economics Discussion Papers em-dp2013-02, Department of Economics, University of Reading.
    3. Kanchana Nadarajah & Gael M Martin & Donald S Poskitt, 2019. "Optimal Bias Correction of the Log-periodogram Estimator of the Fractional Parameter: A Jackknife Approach," Monash Econometrics and Business Statistics Working Papers 7/19, Monash University, Department of Econometrics and Business Statistics.
    4. Victoria Zinde-Walsh, 2008. "Consequences of lack of smoothness in nonparametric estimation (in Russian)," Quantile, Quantile, issue 4, pages 57-69, March.
    5. repec:rdg:wpaper:em-dp2013-02 is not listed on IDEAS
    6. Yoonseok Lee & Yu Zhou, 2015. "Averaged Instrumental Variables Estimators," Center for Policy Research Working Papers 180, Center for Policy Research, Maxwell School, Syracuse University.
    7. repec:hal:journl:peer-00815563 is not listed on IDEAS
    8. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
    9. Valdério A. Reisen & Eric Moulines & Philippe Soulier & Glaura C. Franco, 2010. "On the properties of the periodogram of a stationary long‐memory process over different epochs with applications," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 20-36, January.

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