Local polynomial Whittle estimation of perturbed fractional processes

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• 作者：Per Frederiksen^a ; Frank S. Nielsen^b ; ^d ; ^{fnielsen@creates.au.dk} ; Morten Ø ; rregaard Nielsen^c ; ^d
• 关键词：C22
• 刊名：Journal of Econometrics
• 出版年：2012
• 出版时间：April 2012
• 年：2012
• 卷：167
• 期：2
• 页码：426-447
• 全文大小：420 K

文摘

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 , asymptotically normal for , and if the spectral density is sufficiently smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, . 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.