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Adaptive Local Polynomial Whittle Estimation of Long-Range Dependence

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  • ANDREWS, DONALD W
  • Sun, Yixiao X

Abstract

The local Whittle (or Guassian 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 (Lamda), 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 (Lamda) 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 (Lamda) at zero, up to a logarithmic factor.

Suggested Citation

  • ANDREWS, DONALD W & Sun, Yixiao X, 2002. "Adaptive Local Polynomial Whittle Estimation of Long-Range Dependence," University of California at San Diego, Economics Working Paper Series qt9wt048tt, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt9wt048tt
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    Keywords

    Adaptive estimator; asymptotic bias; asymptotic normality; bias reduction; local polynomial; long memory; minimax rate; optimal bandwidth; Whittle likelihood;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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