Statistical Inference Of High Frequency Integer-Valued Time Series Based On INMA Models

High-frequency data is widely used in finance,medical care,education,and the Internet.For example,the trading volume per minute of the stock market,the number of claims for a product of an insurance company,and the number of students entering and leaving the library every minute.Because high-frequency data can better reflect the true characteristics and high volatility of data in various fields than lower-frequency data.therefore some scholars at home and abroad have begun to use high-frequency data to study stock market transactions.In recent years,integer-valued time series models have attracted the attention of scholars in the processing of high-frequency data,and some meaningful research results have been obtained,in which the appropriate integer-valued time series model is used to study the data characteristics and variation laws of variables particularly important.The main research content of this paper is the parameter estimation of the integer-value moving average model and its application in high frequency data.First,some preliminary knowledge of time series and high frequency data is reviewed,including basic time series models,modeling methods for high frequency data,and some common sparse operations.Secondly,the moment estimation and quasi-likelihood estimation of the integer-value moving average model are studied under the condition that the second-order moment of the innovation sequence is finite.In order to give an analytical form of quasi-likelihood estimation,an approximation method for the innovation sequence is given.Thirdly,two extended forms of the first-order integer-value moving average models are discussed: one is an integer-valued moving average model with explanatory variables.The second is the high-order integer-value moving average model.The estimation problem of the extended model is also discussed.In the empirical analysis,the integer-value moving average model is used to fit the high-frequency intraday trading data of China Guomao stock(stock number:600007).It was found that the model studied had a good effect on the fitting of the data of the group,and this method was more general than the existing method.