Estimation of long memory in integrated variance
AbstractA 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 InfoPaper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2011-11.
Date of creation: 12 Apr 2011
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Realized variance; Long memory; fractional Brownian Motion; Measurement error; Whittle estimator.;
Other versions of this item:
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-04-23 (All new papers)
- NEP-ECM-2011-04-23 (Econometrics)
- NEP-ETS-2011-04-23 (Econometric Time Series)
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- 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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