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.
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Paper provided by EconWPA in its series Econometrics with number
0412006.
Clifford M. Hurvich & Eric Moulines & Philippe Soulier, 2005.
"Estimating Long Memory in Volatility,"
Econometrica,
Econometric Society, vol. 73(4), pages 1283-1328, 07.
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Find related papers by JEL classification: C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: 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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References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Ghysels, E. & Harvey, A. & Renault, E., 1995.
"Stochastic Volatility,"
Papers
95.400, Toulouse - GREMAQ.
Other versions:
Ghysels, E. & Harvey, A. & Renault, E., 1996.
"Stochastic Volatility,"
Cahiers de recherche
9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
Ghysels, E. & Harvey, A. & Renault, E., 1996.
"Stochastic Volatility,"
Cahiers de recherche
9613, Universite de Montreal, Departement de sciences economiques.
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