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

Nonparametric volatility estimation in scalar diffusions: Optimality across observation frequencies

Jakub Chorowski

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

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

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diffusion processes nonparametric estimation sampling frequency spectral approximation


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

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