Estimation of Long Memory in Integrated Variance

Center for Research in Econometrics Analysis of Time Series (CREATES) Working Paper No. 2011-11

33 Pages Posted: 17 Apr 2011

See all articles by Eduardo Rossi

Eduardo Rossi

Department of Economics and Management

Paolo Santucci de Magistris

Aarhus University - CREATES

Date Written: April 12, 2011

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.

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

JEL Classification: C10, C22, C80

Suggested Citation

Rossi, Eduardo and Santucci de Magistris, Paolo, Estimation of Long Memory in Integrated Variance (April 12, 2011). Center for Research in Econometrics Analysis of Time Series (CREATES) Working Paper No. 2011-11, Available at SSRN: https://ssrn.com/abstract=1808619 or http://dx.doi.org/10.2139/ssrn.1808619

Eduardo Rossi

Department of Economics and Management ( email )

Via San Felice 5
27100 Pavia
Italy
++ (Phone)

Paolo Santucci de Magistris (Contact Author)

Aarhus University - CREATES ( email )

Department of Economics and Business Economics
Fuglesangs Allè 4
Aarhus V, 8210
Denmark

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