| With the development of computer storage technology and the increasing popularity of high-speed internet, the cost of collecting, recording, storing and analyzing all types of data samples has been significantly reduced. The sources of data also have become much more extensive, and include original manual records, the development of intelligent database storage, data that is sourced from traditional PCs, and data originating from mobile phones. These technological innovations, which are moving all of us imperceptibly into the age of big data, allow individuals to create their own data and also to enjoy the convenience and efficiency of big data. One example of the utilization of high-frequency data is in the financial markets, in which traders and analysts rely on big data to inform their intraday trading decisions. Such financial data can be subdivided into high-frequency and ultra high-frequency. The sampling frequency of high-frequency data is calculated in hours, minutes and seconds. This data belongs to the category of equal interval sampling data; the frequency is increased for use at the level of intraday trading. Meanwhile, ultra high-frequency data refers to the full register of sample data used in the transaction process; namely, the real-time transaction data. Ultra high-frequency data samples belong to the category of non-traditional data, based on the event itself. When using ultra high-frequency data, the sampling frequency will increase to produce the relevant information; however, increasing the sampling frequency also means that the data will be more influenced by market noise. Ultra high frequency data refers to the population data in the transaction process,that is to say the real time tick by tick data.lt belongs to the non-traditional data structure,while it takes the event itself as the only identity of the data.Comparing to the low frequency data,high frequency data not only has the general ARCH characteristics,such as heavy tail, abnormal distribution,clustering,but also has intraday pattern,discrete value and high correlation characteristics.How to conduct high-frequency and ultra high-frequency data processing and analysis has been the focus of much of the theoretical and empirical research being conducted in the field of financial econometrics.The Chinese stock market is an emerging market in a country that is in the midst of an economic transition. Compared with mature international markets, China’s trading system has not been perfected. Stock price volatility is affected by policy news and speculation; therefore, so our market has some special characteristics that reflect China’s market structure. At the same time, the Chinese stock exchange has launched a level of real-time transaction data (Level-2), which includes intraday transaction records, items commissioned by the market, the sale of the queue, and other information; all of this provides the basic data for the quantitative study of the microstructure of the Chinese stock market. Understanding how to employ high-frequency data modeling can reveal the microstructure and behavior of the Chinese market and guide the development of a reasonable stock trading mechanism and a system by which to effectively supervise it. This would be of great theoretical and practical significance and would help to reduce the information asymmetry of risk, and promote healthy development in the Chinese stock market.In this paper, we use ultra high-frequency data as the research object and discuss it from both a theoretical and an empirical perspective. From a modeling point of view, we focus on the parametric estimation method of a duration model using ultra high-frequency data and intraday pattern scenarios. At the same time, taking market microstructure theory as the empirical theory, we conduct empirical research on the nonlinear characteristics of transaction behavior in the Chinese stock market, combined with the duration model. This paper discusses the following important research points:(1) An SOM clustering algorithm is used to optimize the intraday periodic adjustment problems using the duration model. Intraday periodicity has been widely studied in the context of studies of high-frequency financial data. Intraday periodicity is a dynamic effect characterized by intraday periodic motion; it affects the accuracy of econometric model estimations that contain intraday financial variables. This paper first discusses the importance of intraday periodic adjustment and then introduces self-organizing maps as a solution to intraday periodic adjustment, based on financial ultra high-frequency data. The SOM method features extraction on the basis of neural network learning, which can recognize the dynamic features of high-dimensional data in order to overcome the disadvantage of static periodic adjustment. Finally, a Monte Carlo simulation using an autoregressive conditional duration model will be built to compare the effects of three intraday periodic adjustment methods. The result shows that the SOM method performs effectively and reliably. Therefore, the SOM method may be particularly suited for the analysis of the periodic structure in big data.(2) A comparative analysis of performance by using different random disturbances in ACD model is used to provide reference for the correct specification of the model and the correct parameter estimation method.In this paper, according to the ACD model of different random disturbances, we provide a comparative analysis of the linear generalized least square estimator and the quasi-maximum likelihood estimators at different specifications. The ACD model describes the characteristics of ultra high-frequency data using the hazard function of different random disturbances. Through the Monte Carlo simulation experiment, we discuss the flexibility of exponential distribution, Weibull distribution, Burr distribution and Gamma distribution; we also discuss the statistical properties and performance of the GLS and (Q)MLE estimators. Finally we conduct an empirical study to compare ACD model forecasting under different error disturbances. Both the simulation and empirical results show that the MLE estimator based on Burr distribution exhibits the most stable performance with different datasets, while the GLS method—though it is simple and easy to implement in the case of large samples—provides an estimate that is no less accurate.(3) We study the nonlinear characteristics of the transaction behavior of the Chinese stock market microstructure using the state transition mechanism ACD model.We use the ultra high-frequency data of the Chinese stock market and the dissemination of information as a theoretical basis for our research. Based on the ACD model of the mixed Weibull distribution under the mechanism of smooth transition, we focus on an empirical study of the nonlinear characteristics and identification problem of trading behavior in the Chinese market during the period of the release of the Shanghai-Hong Kong Stock Connect program. The empirical results show that the model can effectively identify informed trading behavior, fundamental trading behavior and uninformed trading behavior. We further find that uninformed trading makes up a larger proportion of trades in the Chinese market; for example, the transition rate of informed trade is lower than that of uninformed trading, while the ratio of informed trading to uninformed trading during the opening and closing times of the market is higher. Our study concludes that the trading behavior of the Chinese stock market has a strong nonlinear character. At the same time, the changing trends of different trading strategies during the starting of the Shanghai-Hong Kong Stock Connect program shows obvious information asymmetry in China’s stock market. Finally, this paper explores the shortcomings of the trading mechanisms of China’s stock market, and explores the potential for improving them.In summary, this paper presents a focused look at the ultra high-frequency data duration model. We discuss intraday periodicity of ultra high-frequency data; our findings may be helpful for those attempting to understand the difference between the high-frequency time series model and traditional time series models. Further, our work may help to reveal the structural characteristics of the high-frequency time series. We summarize the duration model theory comprehensively, and we compare it with the parameter estimation method of the duration model in a scientific and systematic way to provide a reliable reference for the application of the duration model. Finally, we originate the study of the intraday trading behavior of China’s stock market from the perspective of the transformation mechanism of the nonlinear ACD model. Our research may help to improve the trading mechanisms and structure of China’s stock market and promote its healthy development. We believe the work presented in this paper has important theoretical value and practical significance.
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