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.
Highlights
High-frequency financial data, such as data on all intraday transactions from a stock market, are increasingly available
Another significant problem with analysis of high-frequency data is that nonsynchronous observation occurs; namely, we observe the prices of different securities at different time points
We study the asymptotic properties of a maximum-likelihood-type estimator σn with a misspecified model containing noisy, nonsynchronous observations
Summary
High-frequency financial data, such as data on all intraday transactions from a stock market, are increasingly available. To explain empirical evidence, when we model stock price data as a continuous stochastic process, we must assume that the observations contain additional noise Another significant problem with analysis of high-frequency data is that nonsynchronous observation occurs; namely, we observe the prices of different securities at different time points. Misspecified models have not been well-studied for diffusion-type processes with high-frequency observations in a fixed interval, even for models in which neither nonsynchronicity nor market microstructure noise is included. We study the asymptotic properties of a maximum-likelihood-type estimator σn with a misspecified model containing noisy, nonsynchronous observations. It is noteworthy that this study enables us to apply machine learning methodologies to intraday stock highfrequency data analysis under conditions of both nonsynchronicity and market microstructure noise.
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