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Estimating Long Memory in Volatility

Author

Listed:
  • Clifford Hurvich

    (New York University USA)

  • Eric Moulines

    (ENST, Paris, France)

  • Philippe Soulier

    (Universite Paris X, France)

Abstract

We consider semiparametric estimation of the memory parameter in a model which includes as special cases both the long-memory stochastic volatility (LMSV) and fractionally integrated exponential GARCH (FIEGARCH) models. Under our general model the logarithms of the squared returns can be decomposed into the sum of a long-memory signal and a white noise. We consider periodogram-based estimators using a local Whittle criterion function. We allow the optional inclusion of an additional term to account for possible correlation between the signal and noise processes, as would occur in the FIEGARCH model. We also allow for potential nonstationarity in volatility, by allowing the signal process to have a memory parameter d^* >= 1/2. We show that the local Whittle estimator is considtent for d^* in (0,1). We also show that the local Whittle estimator is asymptotically normal for d^* in (0,3/4) and asymptotically recovers the optimal semiparametric rate of convergence for this problem. In particular, if the spectral density of the short memory component of the signal is sufficiently smooth, a convergence rate of n^{2/5-\delta} for d^* in (0,3/4) can be attained, where n is the sample size and \delta > 0 is arbitrarily small. This represents a strong improvement over the performance of existing semiparametric estimators of persistence in volatility. We also prove that the standard Gaussian semiparametric estimator is asymptotically normal if d^*=0. This yields a test for long memory in volatility.

Suggested Citation

  • Clifford Hurvich & Eric Moulines & Philippe Soulier, 2004. "Estimating Long Memory in Volatility," Econometrics 0412006, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpem:0412006
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    References listed on IDEAS

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    More about this item

    Keywords

    LMSV; FIEGARCH;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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