Consistency of MLE for partially observed diffusions, with application in market microstructure modeling
Statistics Theory
2024-12-10 v3 Probability
Trading and Market Microstructure
Statistics Theory
Abstract
This paper presents a tractable sufficient condition for the consistency of maximum likelihood estimators (MLEs) in partially observed diffusion models, stated in terms of stationary distribution of the associated fully observed diffusion, under the assumption that the set of unknown parameter values is finite. This sufficient condition is then verified in the context of a latent price model of market microstructure, yielding consistency of maximum likelihood estimators of the unknown parameters in this model. Finally, we compute the latter estimators using historical financial data taken from the NASDAQ exchange.
Cite
@article{arxiv.2201.07656,
title = {Consistency of MLE for partially observed diffusions, with application in market microstructure modeling},
author = {Sergey Nadtochiy and Yuan Yin},
journal= {arXiv preprint arXiv:2201.07656},
year = {2024}
}