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

2022/01/19 by Sergey Nadtochiy, Yuan Yin, Nadtochiy, Sergey +1 · 1 citation
Economics, Econometrics and Finance · #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications #Trading and Market Microstructure (q-fin.TR)

paper · pdf · doi:10.48550/arxiv.2201.07656

openalex publication_date 2022/01/19 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

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.

Cited by

• Multi-dimensional queue-reactive model and signal-driven models: a unified framework

Related

• Consistency of MLE in partially observed diffusion models on a torus
• Parametric Inference for Nonsynchronously Observed Diffusion Processes in the Presence of Market Microstructure Noise
• Maximum Likelihood Estimation for a Markov-Modulated Jump-Diffusion Model
• Maximum Likelihood Estimation of Diffusions by Continuous Time Markov Chain
• Consistency of the maximum likelihood estimator in hidden Markov models with trends