Estimating Long Memory in Volatility

26 Pages Posted: 3 Nov 2008

See all articles by Clifford M. Hurvich

Clifford M. Hurvich

Stern School of Business, New York University; New York University (NYU) - Department of Information, Operations, and Management Sciences

E. Moulines

Ecole Nationale Superieure des Telecommunications

Philippe Soulier

Université d'Évry

Date Written: February 2002

Abstract

We consider semiparametric estimation of the memory parameter in a modelwhich includes as special cases both the long-memory stochasticvolatility (LMSV) and fractionally integrated exponential GARCH(FIEGARCH) models. Under our general model the logarithms of the squaredreturns can be decomposed into the sum of a long-memory signal and awhite noise. We consider periodogram-based estimators which explicitlyaccount for the noise term in a local Whittle criterion function. Weallow the optional inclusion of an additional term to allow for acorrelation between the signal and noise processes, as would occur inthe FIEGARCH model. We also allow for potential nonstationarity involatility, by allowing the signal process to have a memory parameter d1=2. We show that the local Whittle estimator is consistent for d 2 (0;1). We also show that a modi ed version of the local Whittle estimatoris asymptotically normal for d 2 (0; 3=4), and essentially recovers theoptimal semiparametric rate of convergence for this problem. Inparticular if the spectral density of the short memory component of thesignal is suficiently smooth, a convergence rate of n2=5-δ for d 2(0; 3=4) can be attained, where n is the sample size and δ > 0is arbitrarily small. This represents a strong improvement over theperformance of existing semiparametric estimators of persistence involatility. We also prove that the standard Gaussian semiparametricestimator is asymptotically normal if d = 0. This yields a test forlong memory in volatility.

Suggested Citation

Hurvich, Clifford M. and Moulines, Eric and Soulier, Philippe, Estimating Long Memory in Volatility (February 2002). Statistics Working Papers Series, Vol. , pp. -, 2002. Available at SSRN: https://ssrn.com/abstract=1293614

Clifford M. Hurvich (Contact Author)

Stern School of Business, New York University ( email )

44 West 4th Street
New York, NY 10012-1126
United States

New York University (NYU) - Department of Information, Operations, and Management Sciences

44 West Fourth Street
New York, NY 10012
United States

Eric Moulines

Ecole Nationale Superieure des Telecommunications ( email )

Département TSI / CNRS
46, rue Barrault
F-75634 Paris Cedex 13
France
+33 1 45 81 77 03 (Phone)
+33 1 45 88 79 35 (Fax)

HOME PAGE: http://www.tsi.enst.fr/~moulines/index_eng.html

Philippe Soulier

Université d'Évry ( email )

F-91025 Evry Cedex
France
33 (0)1 69 47 02 28 (Phone)
33 (0)1 69 47 02 18 (Fax)

Register to save articles to
your library

Register

Paper statistics

Downloads
53
Abstract Views
542
rank
387,195
PlumX Metrics