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Local Polynomial Whittle Estimation Of Perturbed Fractional Processes

Frank Nielsen, Morten Nielsen () and Per Houmann Frederiksen
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Per Houmann Frederiksen: Nordea Markets

No 1218, Working Paper from Economics Department, Queen's University

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 in (0,1), asymptotically normal for d in (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, sqrt(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.

Keywords: Bias reduction; local Whittle; long memory; perturbed fractional process; semiparametric estimation; stochastic volatility (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
Date: 2009-09
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https://www.econ.queensu.ca/sites/econ.queensu.ca/files/wpaper/qed_wp_1218.pdf First version 2009 (application/pdf)

Related works:
Journal Article: Local polynomial Whittle estimation of perturbed fractional processes (2012) Downloads
Working Paper: Local polynomial Whittle estimation of perturbed fractional processes (2008) Downloads
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