Testing for Long Memory in Volatility

18 Pages Posted: 31 Oct 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

Philippe Soulier

Université d'Évry

Date Written: 2000

Abstract

We consider the asymptotic behavior of log-periodogram regression estimators ofthe memory parameter in long-memory stochastic volatility models, under the nullhypothesis of short memory in volatility. We show that in this situation, if theperiodogram is computed from the log squared returns, then the estimator is asymptoticallynormal, with the same asymptotic mean and variance that would holdif the series were Gaussian. In particular, for the widely used GPH estimator dGPHunder the null hypothesis, the asymptotic mean of m½dGPH is zero and the asymptoticvariance is pi²/24 where m is the number of Fourier frequencies used inthe regression. This justifies an ordinary Wald test for long memory in volatilitybased on the log periodogram of the log squared returns.

Suggested Citation

Hurvich, Clifford M. and Soulier, Philippe, Testing for Long Memory in Volatility (2000). Statistics Working Papers Series, Vol. , pp. -, 2000. Available at SSRN: https://ssrn.com/abstract=1290974

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

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)

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