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Estimation of long memory in integrated variance

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  • 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.

Suggested Citation

  • Eduardo Rossi & Paolo Santucci de Magistris, 2011. "Estimation of long memory in integrated variance," CREATES Research Papers 2011-11, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2011-11
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    References listed on IDEAS

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    Cited by:

    1. Grassi, Stefano & Santucci de Magistris, Paolo, 2015. "It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 62-78.
    2. Andrea Bucci, 2020. "Realized Volatility Forecasting with Neural Networks," Journal of Financial Econometrics, Oxford University Press, vol. 18(3), pages 502-531.
    3. Ilze Kalnina, 2023. "Inference for Nonparametric High-Frequency Estimators with an Application to Time Variation in Betas," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(2), pages 538-549, April.
    4. La Spada Gabriele & Lillo Fabrizio, 2014. "The effect of round-off error on long memory processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(4), pages 1-38, September.
    5. Morelli, Giacomo & Santucci de Magistris, Paolo, 2019. "Volatility tail risk under fractionality," Journal of Banking & Finance, Elsevier, vol. 108(C).
    6. Christian M. Hafner & Arie Preminger, 2016. "The effect of additive outliers on a fractional unit root test," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 401-420, October.

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    More about this item

    Keywords

    Realized variance; Long memory; fractional Brownian Motion; Measurement error; Whittle estimator.;
    All these keywords.

    JEL classification:

    • 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; Diffusion Processes
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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