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TESTING FOR LONG MEMORY IN VOLATILITY

Published online by Cambridge University Press:  24 September 2002

Clifford M. Hurvich  and
Philippe Soulier
Clifford M. Hurvich
Affiliation:
New York University
Philippe Soulier
Affiliation:
Université d'Evry Val d'Essonne
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Abstract

We consider the asymptotic behavior of log-periodogram regression estimators of the memory parameter in long-memory stochastic volatility models, under the null hypothesis of short memory in volatility. We show that in this situation, if the periodogram is computed from the log squared returns, then the estimator is asymptotically normal, with the same asymptotic mean and variance that would hold if the series were Gaussian. In particular, for the widely used GPH estimator [d with circumflex above]GPH under the null hypothesis, the asymptotic mean of m1/2[d with circumflex above]GPH is zero and the asymptotic variance is π2/24 where m is the number of Fourier frequencies used in the regression. This justifies an ordinary Wald test for long memory in volatility based on the log periodogram of the log squared returns.

Information

Type
Research Article
Information
Econometric Theory , Volume 18 , Issue 6 , December 2002 , pp. 1291 - 1308
Copyright
© 2002 Cambridge University Press

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