Semiparametric Estimation in Continuous-Time: Asymptotics for Integrated Volatility Functionals With Small and Large Bandwidths

36 Pages Posted: 22 Sep 2018 Last revised: 7 Nov 2018

See all articles by Xiye Yang

Xiye Yang

Rutgers, The State University of New Jersey - Department of Economics

Date Written: August 1, 2018

Abstract

This paper studies the estimation of integrated volatility functionals, which is essentially a semiparametric two-step estimation problem in the nonstationary continuous-time setting. Different from the classic i.i.d. or stationary setting, a faster-than-$n^{1/4}$ convergence rate for the first-step nonparametric estimator can not be achieved here. By removing various biases in the second step, we establish a new stochastic equicontinuity condition and show that the proposed estimator is root-$n$ consistent and asymptotically mixed Gaussian, for a wider range of bandwidths than existing ones. Moreover, we employ matrix calculus to obtain a new analytical bias correction and variance estimation method that has computational advantage over existing analytical and Jackknife/simulation-based methods. Comprehensive simulation studies demonstrate that our method has good finite sample performance for a variety of volatility functionals, including quadraticity, determinant, continuous beta, and eigenvalues.

Keywords: Semiparametric Two-Step Estimation, Bias Correction, Integrated Volatility Functionals, Matrix Calculus, Small and Large Bandwidths

JEL Classification: C14

Suggested Citation

Yang, Xiye, Semiparametric Estimation in Continuous-Time: Asymptotics for Integrated Volatility Functionals With Small and Large Bandwidths (August 1, 2018). Available at SSRN: https://ssrn.com/abstract=3243457 or http://dx.doi.org/10.2139/ssrn.3243457

Xiye Yang (Contact Author)

Rutgers, The State University of New Jersey - Department of Economics ( email )

75 Hamilton Street
New Brunswick, NJ 08901
United States

HOME PAGE: http://economics.rutgers.edu/people/474-xiye-yang

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