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Testing For Long Memory In Volatility

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  • Hurvich, Clifford M.
  • Soulier, Philippe

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.

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  • Hurvich, Clifford M. & Soulier, Philippe, 2002. "Testing For Long Memory In Volatility," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1291-1308, December.
    • Handle: RePEc:cup:etheor:v:18:y:2002:i:06:p:1291-1308_18
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    Citations

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    Cited by:

    1. Hsieh, Meng-Chen & Hurvich, Clifford M. & Soulier, Philippe, 2007. "Asymptotics for duration-driven long range dependent processes," Journal of Econometrics, Elsevier, vol. 141(2), pages 913-949, December.
    2. Rosenbaum, Mathieu, 2008. "Estimation of the volatility persistence in a discretely observed diffusion model," Stochastic Processes and their Applications, Elsevier, vol. 118(8), pages 1434-1462, August.
    3. Clifford M. Hurvich & Eric Moulines & Philippe Soulier, 2005. "Estimating Long Memory in Volatility," Econometrica, Econometric Society, vol. 73(4), pages 1283-1328, July.
    4. Karanasos, M. & Kartsaklas, A., 2009. "Dual long-memory, structural breaks and the link between turnover and the range-based volatility," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 838-851, December.
    5. Rohit Deo & Meng-Chen Hsieh & Clifford M. Hurvich & Philippe Soulier, 2007. "Long Memory in Nonlinear Processes," Papers 0706.1836, arXiv.org.
    6. Shao, Xiaofeng & Wu, Wei Biao, 2007. "Local asymptotic powers of nonparametric and semiparametric tests for fractional integration," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 251-261, February.
    7. Duffy, Ken & King, Christopher & Malone, David, 2007. "Ambiguities in estimates of critical exponents for long-range dependent processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 43-52.
    8. J. Arteche, 2012. "Semiparametric Inference in Correlated Long Memory Signal Plus Noise Models," Econometric Reviews, Taylor & Francis Journals, vol. 31(4), pages 440-474.
    9. Luis G. Gorostiza & Reyla A. Navarro & Eliane R. Rodrigues, 2004. "Some Long-Range Dependence Processes Arising from Fluctuations of Particle Systems," RePAd Working Paper Series lrsp-TRS401, Département des sciences administratives, UQO.
    10. Mathieu Rosenbaum, 2006. "Estimation of the Volatility Persistence in a Discretly Observed Diffusion Model," Working Papers 2006-02, Center for Research in Economics and Statistics.

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