On The LAD Estimator For TACD Model With Heavy Tail

With the vigorous development of the stock market,how to grasp the dynamics of the stock market has become a hot topic.The frequency of stock transaction data collection interval will affect the quality of information: the higher the frequency of data collection,the less information loss;the lower the frequency of data collection,the more information loss With the development of computer technology,people can obtain the data with higher and higher sampling frequency,that is,high frequency data or ultra-high frequency data.The study of high-frequency data can help us deepen our understanding of the intraday characteristics of the stock market,and then we can better understand the microstructure of the market.At present,autoregressive conditional duration(ACD)model is the most representative one in the modeling of high-frequency data.However,it is found that there are nonlinear properties and structural mutations in high-frequency data After that,some scholars put forward the idea of threshold into ACD model and used piecewise linearization method to carry out research.Since then,the practical application of threshold autoregressive conditional duration(TACD)model has been started.When estimating the parameters of TACD model,the most commonly used method is maximum likelihood estimation(MLE).When estimating the parameters,it is necessary to assume that the error term obeys a known distribution,and MLE has better statistical properties when the variance of error term is limited However,the financial high-frequency data are often accompanied by peak heavy tailing and the existence of outliers.The variance of these data will show infinite characteristics,which is inconsistent with the assumption that the error variance is finite.Moreover,if the assumed error distribution is not consistent with the actual distribution,the results obtained will also have a large deviation from the actual situation.Aiming at the problem of MLE,this paper uses the least absolute multiplication(LAD)estimation to estimate the parameters of TACD model,and proves the asymptotic normality of the lad estimation under the condition of infinite allowable error variance Then,under the assumption that the error term obeys exponential distribution,Pareto distribution and fréchet distribution,the estimation effects of MLE and LAD under the condition of limited variance and infinite variance are compared.Through the analysis of simulation results,it is found that the average deviation and mean square error of LAD estimation are the smallest,which indicates that the lad estimation results are more robust Finally,the lad estimation is applied to the TACD modeling of Shanghai and Shenzhen stock data,and the price durations of Shanghai airport,COSCO Haineng and Huachuang Anyang are studied respectively.It is found that the AIC result of LAD estimation is less than MLE,which indicates that lad estimation is more effective in modeling the price duration of actual stock market data.