Bernoulli

  • Bernoulli
  • Volume 24, Number 4A (2018), 2934-2990.

Nonparametric volatility estimation in scalar diffusions: Optimality across observation frequencies

Jakub Chorowski

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Abstract

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.

Article information

Source
Bernoulli, Volume 24, Number 4A (2018), 2934-2990.

Dates
Received: April 2016
Revised: December 2016
First available in Project Euclid: 26 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.bj/1522051230

Digital Object Identifier
doi:10.3150/17-BEJ950

Mathematical Reviews number (MathSciNet)
MR3779707

Zentralblatt MATH identifier
06853270

Keywords
diffusion processes nonparametric estimation sampling frequency spectral approximation

Citation

Chorowski, Jakub. Nonparametric volatility estimation in scalar diffusions: Optimality across observation frequencies. Bernoulli 24 (2018), no. 4A, 2934--2990. doi:10.3150/17-BEJ950. https://projecteuclid.org/euclid.bj/1522051230


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