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Edgeworth Expansions for Semiparametric Whittle Estimation of Long Memory

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Liudas Giraitis
Peter M Robinson

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Abstract

The semiparametric local Whittle or Gaussian estimate of the long memory parameter is known to have especially nice limiting distributional properties, being asymptotically normal with a limiting variance that is completely known. However in moderate samples the normal approximation may not be very good, so we consider a refined, Edgeworth, approximation, for both a tapered estimate, and the original untapered one. For the tapered estimate, our higher-order correction involves two terms, one of order 1/vm (where m is the bandwidth number in the estimation), the other a bias term, which increases in m; depending on the relative magnitude of the terms, one or the other may dominate, or they may balance. For the untapered estimate we obtain an expansion in which, for m increasing fast enough, the correction consists only of a bias term. We discuss applications of our expansions to improved statistical inference and bandwidth choice. We assume Gaussianity, but in other respects our assumptions seem mild.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2002/438.

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Date of creation: Sep 2002
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Handle: RePEc:cep:stiecm:/2002/438

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Keywords: Edgeworth expansion; long memory; semiparametric estimation.;

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  1. Marc Henry & Peter M Robinson, 1998. "Long and Short Memory Conditional Heteroscedasticity in Estimating the Memory Parameter of Levels - (Now published in Econometric Theory, 15 (1999), pp.299-336.)," STICERD - Econometrics Paper Series /1998/357, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  2. Donald W.K. Andrews & Yixiao Sun, 2001. "Local Polynomial Whittle Estimation of Long-range Dependence," Cowles Foundation Discussion Papers 1293, Cowles Foundation, Yale University. [Downloadable!]
  3. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August. [Downloadable!] (restricted)
  4. Donald W.K. Andrews & Patrik Guggenberger, 2000. "A Bias-Reduced Log-Periodogram Regression Estimator for the Long-Memory Parameter," Cowles Foundation Discussion Papers 1263, Cowles Foundation, Yale University. [Downloadable!]
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  5. Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, vol. 68(4), pages 931-980, July.
  6. Velasco, Carlos & Robinson, Peter M., 2001. "Edgeworth Expansions For Spectral Density Estimates And Studentized Sample Mean," Econometric Theory, Cambridge University Press, vol. 17(03), pages 497-539, June. [Downloadable!]
  7. Robinson, P. M., 1995. "The approximate distribution of nonparametric regression estimates," Statistics & Probability Letters, Elsevier, vol. 23(2), pages 193-201, May. [Downloadable!] (restricted)
  8. Giraitis, Liudas & Robinson, Peter M. & Samarov, Alexander, 2000. "Adaptive Semiparametric Estimation of the Memory Parameter," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 183-207, February. [Downloadable!] (restricted)
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  1. D. S. Poskitt, 2006. "Properties of the Sieve Bootstrap for Fractionally Integrated and Non-Invertible Processes," Monash Econometrics and Business Statistics Working Papers 12/06, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
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