Author's School

Arts & Sciences

Author's Department

Mathematics

Document Type

Article

Publication Date

10-2017

Originally Published In

Figueroa-López, J. E., & Lee, K. (2017). Estimation of a noisy subordinated Brownian Motion via two-scales power variations. Journal of Statistical Planning and Inference, 189, 16-37. https://doi.org/10.1016/j.jspi.2017.05.004

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 Itô 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.

Comments

This is a preprint version of an article that was later published in Figueroa-López, J. E., & Lee, K. (2017). Estimation of a noisy subordinated Brownian Motion via two-scales power variations. Journal of Statistical Planning and Inference, 189, 16-37. https://doi.org/10.1016/j.jspi.2017.05.004

© 2017 Elsevier B.V. All rights reserved.

DOI

10.1016/j.jspi.2017.05.004

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