The ACD Model With SLAD Estimation And Applications In Shanghai And Shenzhen Stock Markets

With the advancement and development of computer technology,the cost of data storage and recording is getting lower and lower,and people can obtain real-time data of every transaction in the financial market,that is,people can obtain data with higher sampling frequency,which is often called high frequency data or ultra high frequency data.However,the unequal spacing of high frequency data transactions makes traditional econometric models not applicable.For the duration of high frequency data,Engle and Russel(1998)proposed the ACD model.After 20 years of development,the ACD model has been widely used.It is well known that for the estimation of parameters of the ACD model,.the most widely used is the Maximum Likelihood Estimation(MLE).For MLE,only the condition that the variance of the errors are finite is imposed for the consistency and asymptotic normality,and the assumption that the errors obey a known distribution in the estimation process.However,the financial high-frequency data have a heavy-tailed nature.The variance of these data may be infinite,which makes the assumption of finite variance seems inappropriate.Also note that once the previously assumed error distribution does not match the actual distribution,the conclusion will not be reliable.In order to solve the shortcomings of MLE,some scholars have proposed to replace MLE with Least Absolute Delivation(LAD)estimation.Although LAD estimation results are more robust than MLE,LAD estimates give the same weight to the outliers and normal points,which is not poper.To overcoming the shortcomings above,this paper uses the Self-weighted Least Absolute Delivation(SLAD)estimation to estimate the paramet,ers of ACD model,and the asymptotic normality of SLAD estimation is shown under certain regular assumptions.Numerical simulations are then carried out by assuming that the errors obey heavy-tailed distributions including the Pareto distribution,the Burr distribution,and the Frechet distribution.By comparing and analyzing the simu-lation results,it is seem that the MSE of the SLAD estimation is the smallest with the heavy-tailed errors,and the SLAD estimation result is the most robust when there are abnormal values in the data.Finally,SLAD is used for modeling.The trading volume and price duration of three stocks are studied.It is found that the AIC and MSE of the SLAD estimation results are smaller than that of MLE,and LAD,which illustrate that the SLAD estimate is more suitable for the parameter estimation of the ACD model.