Consistency of MLE for partially observed diffusions, with application in market microstructure modeling

TL;DR

This paper establishes a verifiable condition for the consistency of MLEs in partially observed diffusion models, applies it to a market microstructure model, and demonstrates its effectiveness with real NASDAQ data.

Contribution

It provides a new, verifiable condition for MLE consistency in partially observed diffusions and applies it to a practical financial market microstructure model.

Findings

Consistency of MLEs verified in a market microstructure model

Theoretical condition validated with NASDAQ data

MLEs successfully estimated unknown parameters

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.