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Estimation of a noisy subordinated Brownian Motion via two-scales power variations

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  • Jose E. Figueroa-Lopez
  • K. Lee

Abstract

High frequency based estimation methods for a semiparametric pure-jump subordinated Brownian motion exposed to a small additive microstructure noise are developed building on the two-scales realized variations approach originally developed by Zhang et. al. (2005) for the estimation of the integrated variance of a continuous Ito process. The proposed estimators are shown to be robust against the noise and, surprisingly, to attain better rates of convergence than their precursors, method of moment estimators, even in the absence of microstructure noise. Our main results give approximate optimal values for the number K of regular sparse subsamples to be used, which is an important tune-up parameter of the method. Finally, a data-driven plug-in procedure is devised to implement the proposed estimators with the optimal K-value. The developed estimators exhibit superior performance as illustrated by Monte Carlo simulations and a real high-frequency data application.

Suggested Citation

  • Jose E. Figueroa-Lopez & K. Lee, 2017. "Estimation of a noisy subordinated Brownian Motion via two-scales power variations," Papers 1702.01164, arXiv.org.
    • Handle: RePEc:arx:papers:1702.01164
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Andreas Behr & Ulrich Pötter, 2009. "Alternatives to the normal model of stock returns: Gaussian mixture, generalised logF and generalised hyperbolic models," Annals of Finance, Springer, vol. 5(1), pages 49-68, January.
    3. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
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    Cited by:

    1. Qi Wang & Jos'e E. Figueroa-L'opez & Todd Kuffner, 2019. "Bayesian Inference on Volatility in the Presence of Infinite Jump Activity and Microstructure Noise," Papers 1909.04853, arXiv.org.
    2. Jos'e E. Figueroa-L'opez & Cecilia Mancini, 2017. "Optimum thresholding using mean and conditional mean square error," Papers 1708.04339, arXiv.org.
    3. Figueroa-López, José E. & Mancini, Cecilia, 2019. "Optimum thresholding using mean and conditional mean squared error," Journal of Econometrics, Elsevier, vol. 208(1), pages 179-210.

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