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Local polynomial Whittle estimation of perturbed fractional processes

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

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Bias reduction; Local Whittle; Long memory; Perturbed fractional process; Semiparametric estimation; Stochastic volatility;

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  1. Per Frederiksen & Morten Orregaard Nielsen, 2008. "Bias-Reduced Estimation of Long-Memory Stochastic Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(4), pages 496-512, Fall.
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Citations

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Cited by:
  1. Eduardo Rossi & Paolo Santucci de Magistris, 2012. "Estimation of long memory in integrated variance," DEM Working Papers Series 017, University of Pavia, Department of Economics and Management.
  2. Adam McCloskey & Pierre Perron, 2012. "Memory Parameter Estimation in the Presence of Level Shifts and Deterministic Trends," Working Papers 2012-15, Brown University, Department of Economics.
  3. Per Frederiksen & Morten Orregaard Nielsen, 2008. "Bias-Reduced Estimation of Long-Memory Stochastic Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(4), pages 496-512, Fall.
  4. Per Frederiksen & Frank S. Nielsen, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-59, School of Economics and Management, University of Aarhus.
  5. Frank S. Nielsen, 2008. "Local polynomial Whittle estimation covering non-stationary fractional processes," CREATES Research Papers 2008-28, School of Economics and Management, University of Aarhus.

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