Local Polynomial Whittle Estimation of Perturbed Fractional Processes

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. 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 in ‡ate the asymptotic variance of the long memory estimator by a multiplicative constant. We show that the estimator is consistent for d 2 (0; 1), asymptotically normal for d 2 (0; 3=4), and if the spectral density is su¢ ciently smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, p 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. Terms of use: Documents inJEL Classi…cations: C22.

An Overview of Modified Semiparametric Memory Estimation Methods

“…In contrast to the aforementioned authors, Hou and Perron (2014) are the first who provide an extension to account for additive noise and short-memory effects. The modifications are based on the concepts of Andrews and Sun (2004), Hurvich et al (2005) and Frederiksen et al (2012) which follow in the next subsections.…”

“…Smith (2005) and Frederiksen et al (2012) find upward biased estimator suggesting a long-memory process, whereas McCloskey and Perron (2013) find evidence for a spurious long-memory process.…”

“…In contrast to a pure fractional process, the short-run dynamics and long-run behavior of a perturbed fractional process are no longer driven by the same innovation. As defined in Frederiksen et al (2012), a perturbed fractional process can be expressed by a signal-plus-noise model with the signal process being a long-memory process, which is perturbed by an additive noise term. We focus on local Whittle based estimators for perturbed fractional processes and refer to Sun and Phillips (2003) or Arteche (2006) for contributions based on the log-periodogram estimator.…”

“…Extending this survey paper by the estimators of Andrews and Sun (2004), Hurvich et al (2005) and Frederiksen et al (2012) we are considering an additive noise component as well as short-run effects as another form of contamination. All three estimation methods modify the form of the spectral density.…”

“…Hurvich et al (2005) extend the estimator of Hurvich and Ray (2003) that is adding an additional term for capturing the effect of the noise term to the low frequency behavior of the spectral density. The estimator of Frederiksen et al (2012) models the short-run dynamics as well as the influence of an additive noise component by a polynomial and allows for serial dependence in the noise term, in contrast to Frederiksen and Nielsen (2008).…”