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Covariance Estimation and Dynamic Asset-Allocation under Microstructure Effects via Fourier Methodology

In: Financial Econometrics Modeling: Market Microstructure, Factor Models and Financial Risk Measures

Author

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  • Maria Elvira Mancino
  • Simona Sanfelici

Abstract

We analyze the properties of different estimators of multivariate volatilities in the presence of microstructure noise, with particular focus on the Fourier estimator. This estimator is consistent in the case of asynchronous data and is robust to microstructure effects; further, we prove the positive semi-definiteness of the estimated covariance matrix. The in-sample and forecasting properties of the Fourier method are analyzed through Monte Carlo simulations. We study the economic benefit of applying the Fourier covariance estimation methodology over other estimators in the presence of market microstructure noise from the perspective of an asset-allocation decision problem. We find that using Fourier methodology yields statistically significant economic gains under strong microstructure effects. References

Suggested Citation

  • Maria Elvira Mancino & Simona Sanfelici, 2011. "Covariance Estimation and Dynamic Asset-Allocation under Microstructure Effects via Fourier Methodology," Palgrave Macmillan Books, in: Greg N. Gregoriou & Razvan Pascalau (ed.), Financial Econometrics Modeling: Market Microstructure, Factor Models and Financial Risk Measures, chapter 1, pages 3-32, Palgrave Macmillan.
    • Handle: RePEc:pal:palchp:978-0-230-29810-1_1
    DOI: 10.1057/9780230298101_1
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    1. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    2. Silja Kinnebrock & Mark Podolskij, 2008. "An Econometric Analysis of Modulated Realised Covariance, Regression and Correlation in Noisy Diffusion Models," CREATES Research Papers 2008-23, Department of Economics and Business Economics, Aarhus University.
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    5. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Journal of Econometrics, Elsevier, vol. 162(2), pages 149-169, June.
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    11. Mancino, M.E. & Sanfelici, S., 2008. "Robustness of Fourier estimator of integrated volatility in the presence of microstructure noise," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2966-2989, February.
    12. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61.
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    Cited by:

    1. Sanfelici Simona & Uboldi Adamo, 2014. "Assessing the quality of volatility estimators via option pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(2), pages 103-124, April.
    2. Shephard, Neil & Xiu, Dacheng, 2017. "Econometric analysis of multivariate realised QML: Estimation of the covariation of equity prices under asynchronous trading," Journal of Econometrics, Elsevier, vol. 201(1), pages 19-42.

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    More about this item

    Keywords

    Mean Square Error; Covariance Estimation; Forecast Horizon; Microstructure Noise; Quadratic Covariation;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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