Estimation of long memory in integrated variance

Eduardo Rossi and Paolo Santucci de Magistris
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Paolo Santucci de Magistris: School of Economics and Management, Aarhus University, CREATES

No 17, DEM Working Papers Series from University of Pavia, Department of Economics and Management

Abstract: A stylized fact is that realized variance has long memory. We show that, when the instantaneous volatility is a long memory process of order d, the integrated variance is characterized by the same long-range dependence. We prove that the spectral density of realized variance is given by the sum of the spectral density of the integrated variance plus that of a measurement error, due to the sparse sampling and market microstructure noise. Hence, the realized volatility has the same degree of long memory as the integrated variance. The additional term in the spectral density induces a finite-sample bias in the semiparametric estimates of the long memory. A Monte Carlo simulation provides evidence that the corrected local Whittle estimator of Hurvich et al. (2005) is much less biased than the standard local Whittle estimator and the empirical application shows that it is robust to the choice of the sampling frequency used to compute the realized variance. Finally, the empirical results suggest that the volatility series are more likely to be generated by a nonstationary fractional process.

Keywords: Realized variance; Long memory stochastic volatility; Measurement error; local Whittle estimator. (search for similar items in EconPapers)
JEL-codes: C14 C22 C58 (search for similar items in EconPapers)
Pages: 39 pages
Date: 2012-11
New Economics Papers: this item is included in nep-ets
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Citations: View citations in EconPapers (5)

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Related works:
Journal Article: Estimation of Long Memory in Integrated Variance (2014)
Working Paper: Estimation of long memory in integrated variance (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:pav:demwpp:017

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