Nonparametric Modeling Of Trading Volume And Price Duration

Since 1990's,high frequency data with frequency of hours,minutes,seconds or real time has become the hot research topics in modern finance.Because of high frequency data has the characteristics of unequal interval,autocorrelation and intraday pattern,which makes the traditional statistical model based on equal interval data no longer applicable.The ACD model proposed by Engle and Russell(1998)shows that it is feasible for simulation and prediction of high frequency data,so it is widely used in financial markets.At present,many scholars are mainly based on parametric ACD modeling,which needs to know the error distribution and function in advance.Compared with the parametric ACD model,the nonparametric ACD model does not assume the distribution of the random error term and the form of the conditional expectation in advance,and reduces the deviation caused by the misspecification of the parameter model.High frequency financial data often has obvious "fat tail",and often with abnormal value,non parametric ACD model based on N-W kernel estimation and local polynomial are common used,because of the nature of similar estimation,it unable to reduce the influence of outliers,this could result in less robust estimation.In view of this,this paper combines non parametric ACD model with M-estimation,and then propose the nonparametric ACD model local linear M-estimator(or ACD model of nonparametric M-estimator),combined with nonparametric iterative algorithm,we give the expressions of estimation for ACD model of nonparametric M-estimator,which inherits the advantages of nonparameter ACD model also overcomes the disadvantage of un-stabilization.In the random error term follows three different distribution and exists 5%outliers conditions,the stochastic simulation of the ACD model,nonparametric ACD model and ACD model of nonparametric M-estimator is conducted in the paper,After contrasting these methods,we find that the MSE and MAE of ACD model of nonparametric M-estimator is smaller than others,and in the random error obeys fat tail Burr distribution and exists outliers conditions,the reduction of error is more obvious,which shows that ACD model of nonparametric M-estimator can better simulate the data of fat tail and outliers,it apply much more to high frequency data.Finally,this method is applied to the Shanghai stock data,and then research the volume duration and price duration,respectively,the result shows that the error of ACD model of nonparametric M-estimator is minimum and more accurate simulate duration sequence.