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Estimation of long memory in integrated variance

  • Eduardo Rossi

    ()

    (University of Pavia)

  • Paolo Santucci de Magistris

    ()

    (University of Padova and CREATES)

A stylized fact is that realized variance has long memory. We show that, when the instantaneous volatility is driven by a fractional Brownian motion, the integrated variance is characterized by long-range dependence. As a consequence, the realized variance inherits this property when prices are observed continuously and without microstructure noise, and the spectral densities of integrated and realized variance coincide. However, prices are not observed continuously, so that the realized variance is affected by a measurement error. Discrete sampling and market microstructure noise induce a finite-sample bias in the fractionally integration semiparametric estimates. A Monte Carlo simulation analysis provides evidence of such a bias for common sampling frequencies.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2011-11.

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Length: 31
Date of creation: 12 Apr 2011
Date of revision:
Handle: RePEc:aah:create:2011-11
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  16. Haldrup, Niels & Nielsen, Morten Oe., . "Estimation of Fractional Integration in the Presence of Data Noise," Economics Working Papers 2003-10, School of Economics and Management, University of Aarhus.
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  19. Dacorogna, Michael M. & Muller, Ulrich A. & Nagler, Robert J. & Olsen, Richard B. & Pictet, Olivier V., 1993. "A geographical model for the daily and weekly seasonal volatility in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 12(4), pages 413-438, August.
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  24. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
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  26. 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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