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Estimation of long memory in integrated variance

  • Eduardo Rossi

    (Department of Economics and Management, University of Pavia)

  • Paolo Santucci de Magistris

    (School of Economics and Management, Aarhus University, CREATES)

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.

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File URL: http://economia.unipv.it/docs/dipeco/quad/ps/RePEc/pav/demwpp/DEMWP0017.pdf
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Paper provided by University of Pavia, Department of Economics and Management in its series DEM Working Papers Series with number 017.

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Length: 39 pages
Date of creation: Nov 2012
Date of revision:
Handle: RePEc:pav:demwpp:017
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  2. MEDDAHI, Nour, 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Universite de Montreal, Departement de sciences economiques.
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  22. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
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  24. Arteche González, Jesús María, 2010. "Semiparametric inference in correlated long memory signal plus noise models," BILTOKI 2010-04, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
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