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

Teppei Ogihara

Stochastic Processes and their Applications, 2021, vol. 142, issue C, 245-292

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 allows 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.

Keywords: Diffusion processes; High-frequency data; Market microstructure noise; Maximum-likelihood-type estimation; Misspecified model; Neural network (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spa.2021.08.007

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