Estimating Long Memory in Volatility

Clifford Hurvich, Eric Moulines (eric.moulines@polytechnique.edu) and Philippe Soulier
Additional contact information
Clifford Hurvich: New York University USA
Philippe Soulier: Universite Paris X, France

Econometrics from University Library of Munich, Germany

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.

Keywords: LMSV; FIEGARCH (search for similar items in EconPapers)
JEL-codes: C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Pages: 39 pages
Date: 2004-12-14
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-fin
Note: Type of Document - pdf; pages: 39
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Related works:
Journal Article: Estimating Long Memory in Volatility (2005)
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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpem:0412006

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