Adaptive Local Polynomial Whittle Estimation of Long-range Dependence

Donald Andrews () and Yixiao Sun

No 1384, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Keywords: Adaptive estimator; Asymptotic bias; Asymptotic normality; Bias reduction; Local polynomial; Long memory; Minimax rate; Optimal bandwidth; Whittle likelihood (search for similar items in EconPapers)
JEL-codes: C13 C14 C22 (search for similar items in EconPapers)
Pages: 50 pages
Date: 2002-10
New Economics Papers: this item is included in nep-ets
Note: CFP 1080.
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Citations: View citations in EconPapers (3)

Published in Econometrica (2004), 72(2): 569-614

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Journal Article: Adaptive Local Polynomial Whittle Estimation of Long-range Dependence (2004)
Working Paper: Adaptive Local Polynomial Whittle Estimation of Long-Range Dependence (2002)
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