Local polynomial Whittle estimation of perturbed fractional processes

TY - UNPB

T1 - Local polynomial Whittle estimation of perturbed fractional processes

AU - Frederiksen, Per

AU - Nielsen, Frank

AU - Nielsen, Morten Ørregaard

PY - 2008

Y1 - 2008

N2 - We propose a semiparametric local polynomial Whittle with noise (LPWN) estimator of thememory parameter in long memory time series perturbed by a noise term which may be seriallycorrelated. The estimator approximates the spectrum of the perturbation as well as that of theshort-memory component of the signal by two separate polynomials. Including these polynomialswe obtain a reduction in the order of magnitude of the bias, but also in‡ate the asymptoticvariance of the long memory estimate by a multiplicative constant. We show that the estimatoris consistent for d 2 (0; 1), asymptotically normal for d ε (0, 3/4), and if the spectral density isinfinitely smooth near frequency zero, the rate of convergence can become arbitrarily close to theparametric rate, pn. A Monte Carlo study reveals that the LPWN estimator performs well inthe presence of a serially correlated perturbation term. Furthermore, an empirical investigationof the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility thanthe standard local Whittle estimator.

AB - We propose a semiparametric local polynomial Whittle with noise (LPWN) estimator of thememory parameter in long memory time series perturbed by a noise term which may be seriallycorrelated. The estimator approximates the spectrum of the perturbation as well as that of theshort-memory component of the signal by two separate polynomials. Including these polynomialswe obtain a reduction in the order of magnitude of the bias, but also in‡ate the asymptoticvariance of the long memory estimate by a multiplicative constant. We show that the estimatoris consistent for d 2 (0; 1), asymptotically normal for d ε (0, 3/4), and if the spectral density isinfinitely smooth near frequency zero, the rate of convergence can become arbitrarily close to theparametric rate, pn. A Monte Carlo study reveals that the LPWN estimator performs well inthe presence of a serially correlated perturbation term. Furthermore, an empirical investigationof the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility thanthe standard local Whittle estimator.

KW - Bias reduction, local Whittle, long memory, perturbed fractional process, semiparametric estimation, stochastic volatility

M3 - Working paper

BT - Local polynomial Whittle estimation of perturbed fractional processes

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -