Misspecified diffusion models with high-frequency observations and an application to neural networks

TL;DR

This paper develops a new quasi-likelihood method for misspecified diffusion models with high-frequency data, enabling effective application of machine learning, especially neural networks, to financial microstructure analysis.

Contribution

It introduces a quasi-likelihood approach that corrects bias in misspecified diffusion models, facilitating machine learning integration for high-frequency financial data analysis.

Findings

Neural networks outperform polynomial models in volatility prediction.

The proposed method achieves the optimal convergence rate.

Application to Tokyo Stock Exchange data demonstrates practical effectiveness.

Abstract

We study the asymptotic theory of misspecified models for diffusion processes with noisy nonsynchronous observations. Unlike with correctly specified models, the original maximum-likelihood-type estimator has an asymptotic bias under the misspecified setting and fails to achieve an optimal rate of convergence. To address this, we consider a new quasi-likelihood function that arrows constructing a maximum-likelihood-type estimator that achieves the optimal rate of convergence. Study of misspecified models enables us to apply machine-learning techniques to the maximum-likelihood approach. With these techniques, we can efficiently study the microstructure of a stock market by using rich information of high-frequency data. Neural networks have particularly good compatibility with the maximum-likelihood approach, so we will consider an example of using a neural network for simulation studies and empirical analysis of high-frequency data from the Tokyo Stock Exchange. We demonstrate that the neural network outperforms polynomial models in volatility predictions for major stocks in Tokyo Stock Exchange.