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Estimation of long memory in integrated variance

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Author Info

  • Eduardo Rossi

    ()
    (University of Pavia)

  • Paolo Santucci de Magistris

    ()
    (University of Padova and CREATES)

Abstract

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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Bibliographic Info

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

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Realized variance; Long memory; fractional Brownian Motion; Measurement error; Whittle estimator.;

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References

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Cited by:
  1. Gabriele La Spada & Fabrizio Lillo, 2011. "The effect of round-off error on long memory processes," Papers 1107.4476, arXiv.org, revised Mar 2013.

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