Research For Nonparametric ACD Model Based On Kernel Estimate

With the development of technology and improvment of data-capture technology, high frequency data and ultra-high frequency data develope into a rising research direction of financial time series. High Frequency Data is the data that acquisition frequency is hours,minutes or seconds, Ultra-high Frequency Data is the data of real time data acquisition in the trading process. In the stock market, trading duration indicates the time interval of each trade,which is a typical ultra-high frequency data. ACD model is mainly applied in the high frequency data, and can reveal the microstructure of data. Nonparametric method don’t need to make any assumptions about data and models, the form of it is more free; It builds models by the data directly and the choice of smoothing parameter is mainly by data-driven; It has the features of strong adaptive ability, high robustness and accuracy. This paper aims at applying the ACD model combined with the nonparametric method in the stock market of China to get a basic analysis, the main content is as follow:In the theoretical part, the paper introduces the features of high frequency data which are irregularity of time interval, discrete value, huge data size, unequal interval, autocorrelation, and calender effect. Then it states the theory of ACD model emphasisly. According to the different distribution of ie,ACD model can seperate into EACD model,WACD model and GACD model which are the extended model. At last,the paper introduces the kernel estimator belonged to the nonparametric method in detail, combining the ACD model,we get the nonparametric ACD model based on the kernel estimator.In the part of empirical analysis, selecting the inactive stock Minshengyinhang and the active stock Shanghlvxin as the research samples, we get the trading duration data from December 1th to December 5th of the two stocks. First, we pretreat the trading duration data of wiping off the calender effect.From the basic analysis of descriptive statistics and autocorrelation, compared with the data before pretreatment, after pretreatment data’s statistical indicators all decline, and data is more concentrated. However, whether before or after the pretreatment, the data both dont’t follow the Normally Distribution and exist the autocorrelation. Applying the WACD(1,1) and GACD(1,1) to fit the trading duration data of the two stocks,we get the estimation model. According to the result of residual’ACF and Ljung-Box statistics,WACD model and GACD model are more fittable for the active stock Shanghlvxin than the inactive stock Minshengyinhang. Then applying the kernel estimator to fit the trading duration data of the two stocks, the effect of the two forcast curve is ideal, The MSE and MAE are used to test the prediction effects of the three models separately. Seeing from these two index, between the two parametric ACD model, the effect of GACD model for fitting the active stock Shanghlvxin is better,and the error of WACD model for fitting the inactive stock Minshengyinhang is less. In general, compared with the parametric method,the error of two stocks is better with the nonparametric kernel estimator.