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
Date Written: April 12, 2011
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
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