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Testing For Long Memory In Volatility

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Author Info
Hurvich, Clifford M.
Soulier, Philippe

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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 2/24 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.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 18 (2002)
Issue (Month): 06 (December)
Pages: 1291-1308
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Handle: RePEc:cup:etheor:v:18:y:2002:i:06:p:1291-1308_18

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  1. Alejandro Islas Camargo & Francisco Venegas Martínez, 2003. "Pricing Derivatives Securities with Prior Information on Long- Memory Volatility," Economia Mexicana NUEVA EPOCA, , vol. 0(1), pages 103-134, January-J. [Downloadable!]
  2. Clifford Hurvich & Eric Moulines & Philippe Soulier, 2004. "Estimating Long Memory in Volatility," Econometrics 0412006, EconWPA. [Downloadable!]
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  3. Mengchen Hsieh & Clifford Hurvich & Philippe Soulier, 2004. "Asymptotics for Duration-Driven Long Range Dependent Processes," Econometrics 0412009, EconWPA. [Downloadable!]
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This page was last updated on 2009-11-24.

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