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A Modified Nonparametric Prewhitened Covariance Estimator
Author(s) -
Hirukawa Masayuki
Publication year - 2006
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2006.00477.x
Subject(s) - mathematics , estimator , mean squared error , minimum variance unbiased estimator , bias of an estimator , rate of convergence , consistent estimator , efficient estimator , statistics , stein's unbiased risk estimate , computer science , computer network , channel (broadcasting)
. This paper proposes a fully modified version of the spectral matrix estimator (and the long‐run variance estimator as a special case) proposed originally by Xiao and Linton [Journal of Time Series Analysis (2002) Vol. 23, pp. 215–250], and derives its asymptotic results. A striking feature of the modified spectral matrix estimator is to achieve the convergence rate of O ( T −8/9 ) in the mean squared error (MSE), which is usually achieved under the fourth‐order spectral window. However, this estimator does not sacrifice the positive definiteness of the resulting estimate for the rate improvement; it is Hermitian and positive definite in finite samples by construction. The faster convergence rate is established by a multiplicative bias correction of the crude spectral estimator under the second‐order spectral window. The approximations to some sensible definitions of the MSE of the estimator and the bandwidths that minimize the asymptotic MSEs are also derived. Monte Carlo results indicate that for a wide variety of processes the modified spectral matrix estimator reduces the bias without inflating the variance and thus improves the MSE, compared with the crude, bias‐uncorrected estimator.