Open Access
November 2018 Nonparametric volatility estimation in scalar diffusions: Optimality across observation frequencies
Jakub Chorowski
Bernoulli 24(4A): 2934-2990 (November 2018). DOI: 10.3150/17-BEJ950


The nonparametric volatility estimation problem of a scalar diffusion process observed at equidistant time points is addressed. Using the spectral representation of the volatility in terms of the invariant density and an eigenpair of the infinitesimal generator the first known estimator that attains the minimax optimal convergence rates for both high and low-frequency observations is constructed. The proofs are based on a posteriori error bounds for generalized eigenvalue problems as well as the path properties of scalar diffusions and stochastic analysis. The finite sample performance is illustrated by a numerical example.


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Jakub Chorowski. "Nonparametric volatility estimation in scalar diffusions: Optimality across observation frequencies." Bernoulli 24 (4A) 2934 - 2990, November 2018.


Received: 1 April 2016; Revised: 1 December 2016; Published: November 2018
First available in Project Euclid: 26 March 2018

zbMATH: 06853270
MathSciNet: MR3779707
Digital Object Identifier: 10.3150/17-BEJ950

Keywords: Diffusion processes , nonparametric estimation , sampling frequency , spectral approximation

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 4A • November 2018
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