Composite Quantile Regression Estimation For ACD Models With Applications To Chinese Stock Markets

In recent years,the innovation of trading modes in the financial market and the abundance of financial products have made financial high-frequency data a current research hotspot.Since transactions in the financial market are all random,irregular transaction interval(also called duration)data is produced,which contains a large amount of market microstructure information(such as time-varying,clustering,etc.).Through the study of duration,we can discover the behavioral structure of intraday transactions and better understand the microstructure of the market.In current studies,autoregressive conditional duration(ACD)models are mostly used to describe the evolution of duration.When modeling and estimating with the ACD model,most of them use the maximum likelihood estimation(MLE)method,and MLE often needs to assume that the error term obeys a certain known distribution before estimating,and its variance needs to be finite.In fact,financial high-frequency data usually contains more disturbance information,which is unstable and has a heavy-tailed nature in the short term,and the variance of these data may even tend to infinity,which makes the estimation results of MLE less reliable.Later,some scholars proposed to use quantile regression(QR)to estimate the ACD model.This method does not need to assume the error term distribution in advance and is not sensitive to outliers.It describes the explanation by using conditional distribution functions at different quantiles.The general rule that the variable changes with the response variable,but the deviation of part of the quantile will lead to missing information,and the estimated result will have a big deviation from the actual.Aiming at the shortcomings of MLE and QR estimation,this paper uses the composite quantile regression(CQR)method to estimate the ACD model.This paper first theoretically proves the consistency and asymptotic normality of the CQR estimation,and then uses MLE,QR(0.5)and CQR estimation to estimate the parameters of the ACD model with different error terms.Results of the three methods found that regardless of the variance of the error term distribution is finite or not,the effect of CQR estimation is the best overall.Finally,this paper applies CQR estimation to the ACD modeling of stocks,and conducts empirical research and analysis on the trading volume duration and price duration of two representative stocks.The results show that CQR estimation can fit the duration well.Compared with the other two estimation methods,CQR estimation is more effective for modeling duration.