Bernoulli

  • Bernoulli
  • Volume 24, Number 4B (2018), 3318-3383.

Parametric inference for nonsynchronously observed diffusion processes in the presence of market microstructure noise

Teppei Ogihara

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Abstract

We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of maximum-likelihood- and Bayes-type estimators based on it. We also prove the local asymptotic normality of the model and asymptotic efficiency of our estimator when the diffusion coefficients are deterministic and noise follows a normal distribution. We conjecture that our estimator is asymptotically efficient even when the latent process is a general diffusion process. An estimator for the quadratic covariation of the latent process is also constructed. Some numerical examples show that this estimator performs better compared to existing estimators of the quadratic covariation.

Article information

Source
Bernoulli, Volume 24, Number 4B (2018), 3318-3383.

Dates
Received: December 2015
Revised: April 2017
First available in Project Euclid: 18 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.bj/1524038756

Digital Object Identifier
doi:10.3150/17-BEJ962

Mathematical Reviews number (MathSciNet)
MR3788175

Zentralblatt MATH identifier
06869878

Keywords
asymptotic efficiency Bayes-type estimation diffusion processes local asymptotic normality market microstructure noise maximum-likelihood-type estimation nonsynchronous observations parametric estimation

Citation

Ogihara, Teppei. Parametric inference for nonsynchronously observed diffusion processes in the presence of market microstructure noise. Bernoulli 24 (2018), no. 4B, 3318--3383. doi:10.3150/17-BEJ962. https://projecteuclid.org/euclid.bj/1524038756


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