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Adaptive Local Polynomial Whittle Estimation of Long-range Dependence

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Author Info
Donald W.K. Andrews () (Cowles Foundation, Yale University)
Yixiao Sun (UCLA, San Diego)

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Abstract

The local Whittle (or Gaussian semiparametric) estimator of long range dependence, proposed by Kunsch (1987) and analyzed by Robinson (1995a), has a relatively slow rate of convergence and a finite sample bias that can be large. In this paper, we generalize the local Whittle estimator to circumvent these problems. Instead of approximating the short-run component of the spectrum, phi(lambda), by a constant in a shrinking neighborhood of frequency zero, we approximate its logarithm by a polynomial. This leads to a "local polynomial Whittle" (LPW) estimator. We specify a data-dependent adaptive procedure that adjusts the degree of the polynomial to the smoothness of phi(lambda) at zero and selects the bandwidth. The resulting "adaptive LPW" estimator is shown to achieve the optimal rate of convergence, which depends on the smoothness of phi(lambda) at zero, up to a logarithmic factor.

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File URL: http://cowles.econ.yale.edu/P/cd/d13b/d1384.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1384.

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Length: 50 pages
Date of creation: Oct 2002
Date of revision:
Publication status: Published in Econometrica (2004), 72(2): 569-614
Handle: RePEc:cwl:cwldpp:1384

Note: CFP 1080.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Adaptive estimator; Asymptotic bias; Asymptotic normality; Bias reduction; Local polynomial; Long memory; Minimax rate; Optimal bandwidth; Whittle likelihood;

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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  1. Violetta Dalla & Liudas Giraitis & Javier Hidalgo, 2006. "Consistent estimation of the memory parameterfor nonlinear time series," STICERD - Econometrics Paper Series /2006/497, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  2. Nuno Cassola & Claudio Morana, 2007. "Comovements in Volatility in the Euro Money Market," ICER Working Papers 7-2007, ICER - International Centre for Economic Research. [Downloadable!]
  3. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, School of Economics and Management, University of Aarhus. [Downloadable!]
  4. Claudio Morana, 2006. "Multivariate modelling of long memory processes with common components," ICER Working Papers 40-2006, ICER - International Centre for Economic Research. [Downloadable!]
  5. Nuno Cassola & Claudio Morana, 2006. "Comovements in volatility in the euro money market," Working Paper Series 703, European Central Bank. [Downloadable!]
  6. Katsumi Shimotsu, 2006. "Simple (but effective) tests of long memory versus structural breaks," Working Papers 1101, Queen's University, Department of Economics. [Downloadable!]
  7. Frank S. Nielsen, 2009. "Local Whittle estimation of multivariate fractionally integrated processes," CREATES Research Papers 2009-38, School of Economics and Management, University of Aarhus. [Downloadable!]
  8. Patrik Guggenberger & Yixiao Sun, 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 2004-14, Department of Economics, UC San Diego. [Downloadable!]
  9. Yixiao Sun, 2005. "Adaptive Estimation of the Regression Discontinuity Model," Econometrics 0506003, EconWPA. [Downloadable!]
  10. Javier Hualde & Peter M Robinson, 2006. "Semiparametric Estimation of Fractional Cointegration," STICERD - Econometrics Paper Series /2006/502, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
  11. Nordman, Dan Nordman & Sibbertsen, Philipp & Lahiri, Soumendra N., 2005. "Empirical likelihood confidence intervals for the mean of a long-range dependent process," Diskussionspapiere der Wirtschaftswissenschaftlichen Fakultät der Universität Hannover dp-327, Universität Hannover, Wirtschaftswissenschaftliche Fakultät. [Downloadable!]
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