Statistical Analysis And Empirical Research On Logarithmic Auto-regressive Conditional Duration Models

In the face of high-frequency financial market data with high frequency and irregular transaction time intervals,traditional econometric models are no longer applicable.In order to solve the above problems,the auto-regressive conditional duration(ACD)models use the characteristics of financial high-frequency data to build models with irregular time durations,which has attracted much attention from scholars at home and abroad.Logarithmic auto-regressive conditional duration(Log-ACD)models are one of the important extended forms of ACD models,which describe the nonlinear relationship between time durations and their conditional expectations.Many empirical studies have shown that the models have a significant effect on the analysis of the microstructure of the financial market.This paper will conduct theoretical and empirical research on the Log-ACD models.This paper first introduces the forms of the ACD models and the Log-ACD models,and briefly describes the development process of the duration models.Secondly,the statistical characteristics of the least square estimators of Log-ACD models parameters and the empirical likelihood ratio statistic are proposed.Thirdly,an improved semi-parametric estimating method,the combined estimation functions(CEF)method is discussed,and the theoretical application and statistical inference of the auto-regressive models with time-varying variance based on the combined estimation functions are given.Finally,use real stock trading data to conduct empirical research.After research,the following conclusions are obtained: First,the parameter estimators of the Log-ACD models are obtained using the least square method,whose asymptotic normality are given.Second,the parameter estimators of the Log-ACD models are obtained using the empirical likelihood method,and it is proved that the empirical likelihood ratio test statistic follows the asymptotic chi-square distribution.Third,the estimators of the combined estimation functions of the auto-regressive models parameters with time-varying variance have asymptotic consistency,which asymptotically follow the normal distribution as the sample size increasing.Fourth,numerical simulation and empirical research show that in the face of simulated data with the same variance and time-varying variance and real stock transaction data,the fitting effect and predictive ability of combined estimation functions are slightly better than the pseudo-maximum similarity.Fifth,empirical research have found that under the condition that the Log-ACD models lags by one order,the Beta distribution has better applicability.