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Local polynomial Whittle estimation of perturbed fractional processes

  • Frederiksen, Per
  • Nielsen, Frank S.
  • Nielsen, Morten Ørregaard

We propose a semiparametric local polynomial Whittle with noise estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the log-spectrum of the short-memory component of the signal as well as that of the perturbation by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also inflate the asymptotic variance of the long memory estimator by a multiplicative constant. We show that the estimator is consistent for d∈(0,1), asymptotically normal for d∈(0,3/4), and if the spectral density is sufficiently smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, n. A Monte Carlo study reveals that the proposed estimator performs well in the presence of a serially correlated perturbation term. Furthermore, an empirical investigation of the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility than the standard local Whittle (with noise) estimator.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 167 (2012)
Issue (Month): 2 ()
Pages: 426-447

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Handle: RePEc:eee:econom:v:167:y:2012:i:2:p:426-447
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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