The Nonparametric Conditional Autoregressive Range Model And Its Application

Recently,The securities market of China is in an era,which opportunity and risk can coexist.Its investment and financing environment is very complex.It is very important for the securities market of China how to let the investors effectively control and manage the investment risk in the market.Since the securities market produced,its main characteristics is volatilities in prices.The stakeholders are very concerned of how to accurately describe the price of the securities market and dertermine the market’s future return. Therefor,the research of volatility will have an very important theoretical significance and application value.As is known to all, research volatility in the fanincal market has been widely concerned by the scholars in the theory and application field.It has become an important issue in the field of modern financial economics and econometrics.In the1950s,volatility has played an important role in the CAPM and OPT.In a word,volatility not only has made an important influence to the investor’s investment behavior but also has been widely used in the asset pricing, performance evaluation, and other areas of the economics. The scholars at home and abroad have widely researched the volatility in the financial market and their research contents not only have involved the multivariate GARCH model but also the parameteric,nonparametric and semiparametric GARCH model.The scholars at home and abroad about the research of range in the financial market in not many,whose research contents most stayed in the parameteric CARR model and seldomly involved in the nonparametric CARR model.The related literatures at home and abroad point that rang can. describe the volatility in the financial markets better than volatility.Therefore.this paper will both use the relationship between the range and the volatility and combine with the parameteric CARR model and the nonparametric GARCH model propose the nonparametric CARR model and its uniform convergence estimation algorithm in the weaker condition. This paper will also certificate the consistency of the estimate algorithm.Then,this paper will compare the fitted ability of the parameteric CARR model and the nonparameteric CARR model by simulation experiment and empirical example.On the one hand,it can enrich the research contents and research method in the field of financial econometrics, time series analysis and so on.On the other hand,combined with the current situation of the securities market in China, the results of empirical example have an important practical application value in understanding investors,the influence of market trading activities in the market structure and transaction system,perfecting the supervision measures and effectively improving the quality of transactions in the securities market.In this paper,the main structure arrangement as follows:First,theoretical part.First of all,this paper will introduce the CARR model and its parameteric estimation algorithm.Second, this paper will both use the relationship between the range and the volatility and combine with the parameteric CARR model and the nonparametric GARCH model propose the nonparametric CARR model and its uniform convergence estimation algorithm in the weaker condition,then certificate the consistency of the estimate algorithm.Second,simulation experiment.In order to better simulate the range sequences and leverage effect in the financial market and strengthen the effectiveness and scientific nature of the argument,this paper will generate the range sequences and the real volatility by three kinds of data generation processs and two kinds of residual distribution whose length is5O0.Then,calculate the data generation process500times and compare the fitted ability of the parameteric CARR model and the nonparameteric CARR model by predictive ability evaluation indexs.This part through simulation experiment proves that the nonparametric CARR(1,1) model has bettter fitted ability than the parametric CARR(1,1) model.This part lays a solid theoretical basis for using the parametric CARR(1,1) model and the nonparametric CARR(1,1) in empirical example.Third, empirical example.This paper will select the CSI300Index as the research select and divide the sample into estimation sample and prediction sample.Then,this paper will compare the fitted ability of the parametric CARR(1,1) model and the nonparametric CARR(1,1) model by descriptive statistical characteristic analysis,model estimation and predictive ability evaluation indexs.This part through empirical example proves that the nonparametrica CARR(1,1) model can better fits the CSI300Index’s volatility than the parametric CARR(1,1) model.The steps are layer by layer and progressive interlocking. This papercarries out a systematic study focusing on the parametric CARR(1,1) model and the nonparametric CARR(1.1) model and obtains the following important conclusions:First,the estimation algorithm of the nonparametric CARR model has the consistency.Second,no matter by what kind of data generation process and residual distribution,after500times loop calculation,the predition error of the nonparametric CARR(1,1) model is less than the parametric CARR(1,1) model.No matter by what kind of data generation process.when the residual obey Weibull(1,1.5) distribution,the decrease degree of the nonparametric CARR(1,1) model’s predition error is greater than the parametric CARR(1,1) model.No matter by what kind of data generation process,when the residual obey Weibull(1,1.5) distribution the predition error of the nonparametric CARR(1,1) model is less than the predition error of the parametric CARR(1,1) model whose residual obey exp(1) distribution.Third,the basis statistical charateristics show tha the range has obvious volatility clustering,high order ARCH effect,positive bais and distribution diffusion.Fourth,the estimation sample has different degree correlation,some have a short memory and some have a long memory. The autocorrelation coefficient and partial autocorrelation coefficient gradually reduce when the lag order gradually increase. With the increase of lag order,the Ljung-Box Q gradually increase.Fifth,by estimating the parametric CARR(1,1) model in the period sample,we find that under the5%significance level,the t value of the coefficients are significant and the parametric CARR(1,1) model can well fit the CSI300Index.The CSI300Index has strong volatility clustering.Sixth,predition ability evaluation indexs and MZ regression equation show that no matter what realized volatility adopt by what kind of way,the nonparametric CARR(1,1) model can better fit the CSI300Index than the parametric CARR(1,1) model.Compared with the other papers, the paper has the following characteristics:First, this paper uses the relationship between the range and the volatility and combine with the parameteric CARR model and the nonparametric GARCH model propose the nonparametric CARR model and its uniform convergence estimation algorithm in the weaker condition,then certificate the consistency of the estimate algorithm.This part puts the CARR model from parametra area to nonparametra area and propose a new model and an estimation algorth.Second,this paper firstly compares the fitted ability of the parametric CARR(1,1) model and the nonparametric CARR(1,1) model by simulation experiment.In order to better simulate the range sequences and leverage effect in the financial market and strengthen the effectiveness and scientific nature of the argument,this paper compares the fitted ability of the parametric CARR(1,1) model and the nonparametric CARR(1,1) model by three kinds of data generation process and two kinds of residual distribution,find the nonparametric CARR(1,1) model can better fit the real volality than the parametric CARR(1,1) model. This part lays a solid theoretical basis for using the parametric CARR(1,1) model and the nonparametric CARR(1,1) in empirical example.Third,this paper firstly uses the parametric CARR(1,1) model and the nonparametric CARR(1,1) in the CSI300Index.By predictive ability evaluation indexs and MZ regression equation,we find that no matter what realized volatility adopt by what kind of way,the nonparametric CARR(1,1) model can better fit the CSI300Index than the parametric CARR(1,1) model.This paper is supported by the2011National Natural Foundation of China (71101118) and the2009Education Humanities and Social Science Research Youth Fund (09YJC910009).