非参数条件自回归极差模型及其应用

发布时间：2018-01-17 22:19

本文关键词：非参数条件自回归极差模型及其应用　出处：《西南财经大学》2013年硕士论文　论文类型：学位论文

【摘要】：近几年,我国证券市场正处在一个机遇和风险并存的时代,投融资环境十分地复杂,投资者如何有效地控制和管理其在股票市场上的投资风险,起着关键性的作用。证券市场自产生以来就以其价格的波动为主要特征,如何准确地描述证券市场的价格以及确定市场未来收益率的情况是证券市场各利益主体所关心的问题。因此,对波动性的研究具有重要的理论意义与应用价值。众所周知,用波动率来刻画金融市场的波动性,在理论领域和应用领域都受到了国内外学者的广泛关注,成为现代金融经济学和计量经济学领域的重要课题。上世纪50年代,波动率就在资本资产定价模型和期权定价模型中扮演着重要的角色。总之,波动率不但对投资者的投资行为产生了重要影响,而且还在资产价格确定、绩效评估等经济学领域得到了普遍的应用。虽然国内外学者对于用波动率来刻画金融市场波动性方面的研究已经十分地广泛,研究内容不仅涉及到了一元、多元GARCH模型,还涉及到了参数、非参数和半参数GARCH模型。国内外学者对于用极差来刻画金融市场波动性的研究却不多,这方面的研究多数停留在参数CARR模型领域,而在非参数CARR模型领域却很少涉及。国内外相关文献指出,极差比波动率能够更好地刻画金融市场的波动性。因而,本文将利用极差和波动率的关系,结合参数CARR模型和非参数GARCH模型的思想,提出非参数CARR模型及其在比较弱的条件下的一致收敛估计方法,并对其估计的一致性进行证明；然后分别从模拟角度和实证角度,对参数CARR(1,1)模型和非参数CARR(1,1)模型进行模拟研究和实证分析,研究哪个模型能够更好地刻画金融市场的波动性。一方面,有利于充实金融市场计量经济学、时间序列分析和高频数据的研究内容和研究方法；另一方面,结合当前我国证券市场的情况考虑,实证研究结果对于了解投资者、市场交易活动受市场结构和交易制度的影响程度以及完善我国证券市场的监管措施,有效地提高市场的交易质量提供了科学的决策依据,具有重要的实际应用价值。本文的主要结构安排如下：第一,理论部分。首先,介绍参数CARR模型及其估计方法；然后,利用极差和波动率之间的关系,结合参数CARR模型和非参数GARCH模型的思想,提出非参数CARR模型及其在比较弱的条件下的一致收敛估计方法,并对其估计的一致性进行证明。该部分将CARR模型由参数领域向非参数领域进行了扩展,为本文在模型和估计方法上的创新。第二,模拟研究。为了能够更好地模拟金融市场的极差序列和杠杆效应以及加强论证的有效性和科学性,本文将通过3种数据生成过程和2种扰动项分布分别生成长度n=500的极差序列和真实波动率序列；然后将上述数据生成过程循环计算500次,运用预测能力评价指标比较参数CARR (1,1)模型和非参数CARR (1,1)模型的拟合能力,研究哪个模型能够更好地拟合真实波动率序列。该部分通过模拟发现了非参数CARR (1,1)模型的拟合能力优于参数CARR (1,1)模型,为后面将参数CARR (1,1)模型和非参数CARR(1,1)模型运用到我国沪深300指数中进行具体的实证研究,奠定了理论基础。第三,实证分析。本文将选取沪深300指数日极差序列作为研究对象,将整个样本分为样本期内和样本期外两部分,从描述性统计特征分析、模型估计、预测能力评价指标和MZ回归方程几个方面比较参数CARR (1,1)模型和非参数CARR (1,1)模型样本期内和样本期外的预测能力。该部分从实证角度证明了非参数CARR (1,1)模型的拟合能力优于参数CARR (1,1)模型,对模拟结果进行了验证,结果更具有说服力。以上几个步骤逐层递进、环环相扣。围绕参数CARR (1,1)模型和非参数CARR (1,1)模型进行了系统的研究,得出以下几点重要结论。第一,非参数CARR模型的估计方法具有在比较弱的条件下一致收敛的性质。第二,无论通过哪种数据生成过程和扰动项分布,经过m=500次循环计算后,得到的非参数CARR (1,1)模型的预测误差均要小于参数CARR (1,1)模型的预测误差；无论通过哪种数据生成过程,当扰动项服从Weibull(1,1.5)分布时得到的极差序列和真实波动率序列,通过m=500次循环计算后所得到的非参数CARR (1,1)模型的预测误差的减少程度大于参数CARR (1,1)模型的预测误差的减少程度(个别指标除外)；无论通过哪种数据生成过程,当扰动项服从Weibull(1,1.5)分布时得到的极差序列和真实波动率序列,通过m=500次循环计算后所得到的参数CARR (1,1)模型和非参数CARR (1,1)模型的预测误差均要小于扰动项服从指数分布exp(1)时的预测误差。第三,基本统计特征显示,沪深300指数极差序列具有明显的波动聚集现象和高阶的ARCH效应,存在正偏、分布扩散和拖尾的现象。第四,样本期内的极差具有不同程度的自相关性,有的具有短记忆性,有的具有长记忆性和可持续性；自相关系数和偏相关系数大致上呈现出随着滞后阶数的增加逐渐衰减的特点,其中偏相关系数的衰减程度大于自相关系数的衰减程度；Ljung-Box Q统计量呈现出随着滞后阶数的增加逐渐增加的特点。第五,通过对参数CARR (1,1)模型进行样本期内的极大似然估计,发现在5%的显著性水平下,估计参数的T值均是显著的；经过参数CARR(1,1)模型过滤之后,样本期内的极差序列已经不存在显著地异方差性；参数CARR(1,1)模型可以很好地拟合样本期内沪深300指数的波动性；沪深300指数存在很强的波动聚集现象。第六,预测能力评价指标和MZ回归方程显示,无论“己实现波动率”采用哪种方式测度,样本期内和样本期外非参数CARR (1,1)模型的预测能力均优于参数CARR (1,1)模型。与其他文章相比,本文的创新点主要基于以下三方面：第一,本文利用极差和波动率之间的关系,结合参数CARR模型和非参数GARCH模型的思想,首次提出非参数CARR模型及其在比较弱的条件下的一致收敛估计方法,并对其估计方法的一致性进行证明。该部分将CARR模型由参数领域向非参数领域进行了扩展,为本文在模型和估计方法上的理论创新。第二,首次对参数CARR (1,1)模型和非参数CARR (1,1)模型进行模拟研究。为了能够更好地模拟金融市场的极差序列和杠杆效应以及加强论证的有效性和科学性,本文通过选取不同的数据生成过程和扰动项分布来对参数CARR(1,1)模型和非参数CARR(1,1)模型进行模拟研究和预测能力评价,通过模拟发现非参数CARR (1,1)模型的拟合能力优于参数CARR (1,1)模型,能够更好地拟合真实波动率序列。该部分为将非参数CARR (1,1)模型运用到金融市场中进行具体的实证研究奠定了良好的理论基础。第三,首次将非参数CARR (1,1)模型运用到我国沪深300指数极差序列中进行实证研究。本文将沪深300指数极差序列分为样本期内和样本期外两部分,通过将参数CARR (1,1)模型和非参数CARR (1,1)模型运用到我国沪深300指数极差序列中进行基本统计特征分析、模型估计和预测能力评价,一方面发现了沪深300指数极差序列存在显著的正偏、分布扩展和波动聚集的现象；另一方面,通过对参数CARR (1,1)模型和非参数CARR (1,1)模型进行样本期内和样本期外的预测能力评价和MZ回归,发现非参数CARR(1,1)模型的预测能力优于参数CARR (1,1)模型,能够更好地刻画我国沪深300指数的波动性。该部分从实际应用角度对模拟结果进行验证,结果更具有说服力。本文由2011年度国家自然科学基金青年科学基金项目《新兴订单驱动市场非负值金融时间序列的乘积误差建模及应用研究》(71101118)和2009年度教育部人文社会科学研究青年基金项目《新兴订单驱动市场金融持续时间的统计分析及其应用》(09YJC910009)资助完成。
[Abstract]:In recent years, China's securities market is in a era of opportunities and risks, the financing environment is very complex, investors how to effectively control and manage the investment risk in the stock market, plays a key role. The stock market has been in the price fluctuation of main features how to accurately describe the securities market, the price and the market determine the future yield are the interests of the main stock market concerns. Therefore, the study of volatility has important theoretical significance and practical value.
As everyone knows, the volatility of volatility to describe the financial market, in the field of theory and application have attracted the attention of scholars at home and abroad, has become an important topic in modern financial economics and Econometrics field. In 50s the last century, volatility in the pricing model and option pricing model of capital assets plays an important role. In short, volatility not only has important influence on the investment behavior of investors, but also asset price determination, performance evaluation and other areas of economics has been widely used. Although scholars at home and abroad with the wave rate to describe the volatility of financial market is very wide, not only involves the contents of one yuan the multivariate GARCH model, and also involves parameters, non parametric and semi parametric GARCH model. Scholars to describe the volatility of financial market with the poor But not much, most of this research stays in the domain of parameter CARR model, but is rarely involved in the nonparametric CARR model domain.
The related literature at home and abroad, pointed out that the fluctuation range than the volatility can better describe the financial market. Therefore, this paper will use the relationship between range and volatility, combined with the parameters of CARR model and non parametric GARCH model, the nonparametric CARR model and uniform convergence in a weak estimation method under, and the consistency of the estimates are proved; then from the simulation and empirical point of view, the parameters of CARR (1,1) model and non parameter CARR (1,1) model for simulation study and empirical research on the volatility of which model can better depict financial market. On the one hand, is conducive to enrich the financial market econometrics, research contents and research methods of time series analysis and high frequency data; on the other hand, considering the current situation of China's securities market, the empirical results for the understanding of investors, market transactions It is a scientific decision basis for us to be influenced by the market structure and trading system and improve the regulation measures in China's securities market, and effectively improve the trading quality of the market. It has important practical application value. The main structure of this paper is as follows:
First, the theoretical part. Firstly, introducing the model and parameter estimation method of CARR; then, the relationship between range and volatility, combined with the parameters of CARR model and non parametric GARCH model, the nonparametric CARR model and uniform convergence in the weak condition estimation method, and the consistency of estimation this part will be proved. The CARR model parameters from the field to the non parameter field is extended to the innovation in the model and estimation methods.
Second, simulation research. In order to poor sequence and leverage effect can better simulate the financial market and strengthen the demonstration of effective and scientific, the 3 kinds of data generation process and 2 kinds of disturbance distribution respectively generate length n=500 sequence and the range of actual volatility sequence; then the data generation process cycle calculation 500, the use of prediction ability evaluation index comparison of parameters of CARR (1,1) model and non parameter CARR (1,1) model fitting ability, which study model can better fit the actual volatility sequence. This part is found through the dynamic simulation of non parameter CARR (1,1) fitting ability is better than the parameters of the CARR model (1,1) model for behind the parameters of CARR (1,1) model and non parameter CARR (1,1) model is applied to the empirical research of China's Shanghai and Shenzhen 300 index, which lay a theoretical foundation.
Third, empirical analysis. This paper will select the Shanghai and Shenzhen 300 index range sequence as the research object, the entire sample is divided into two parts of the sample period and sample period, from the characteristics of descriptive statistics analysis, model estimation, prediction ability evaluation index and MZ regression equation on compare parameters of CARR (1,1) model and non parametric CARR (1,1) model of sample period and sample period. In this part, from the perspective of the empirical proof of non parameter CARR (1,1) fitting ability is better than the parameters of the CARR model (1,1) model, the simulation results were verified, the results more convincing.
The above steps step by step, interlocking. The following conclusions are drawn from the parametric CARR (1,1) model and the non parametric CARR (1,1) model.
First, the estimation method of the nonparametric CARR model has the property of uniform convergence under relatively weak conditions.
Second, no matter what kind of data through the production process and the disturbance distribution, after m=500 cycles after the calculation, the parameters of CARR (1,1) prediction error model parameters were less than CARR (1,1) prediction error model; the generating process of either data, when the disturbance obeys the Weibull distribution (1,1.5) the range of sequences and real volatility series, non parametric CARR obtained by m=500 cycles after computation (1,1) to reduce the degree of model prediction error is larger than the parameters of CARR (1,1) to reduce the degree of model prediction error (the individual indicators except); either the data generation process, when the disturbance to Weibull (1,1.5) distribution obtained when the range data and real volatility series, CARR parameters obtained by m=500 cycles after calculating (1,1) model and non parameter CARR (1,1) model prediction errors are less than the disturbance service The prediction error from the exponential distribution of exp (1).
Third, the basic statistical characteristics show that the Shanghai and Shenzhen 300 index extreme sequence has obvious volatility aggregation phenomenon and high-order ARCH effect, and there are positive bias, distribution diffusion and tailing phenomenon.
Fourth, poor sample period has different degree of correlation, with some short memory, some has long memory and sustainability; self correlation coefficient and partial correlation coefficient generally showed with the increase of the characteristics of lag order decays, the attenuation degree of the partial correlation coefficient is greater than the degree of attenuation of autocorrelation the coefficient of Ljung-Box; Q statistics show with the characteristics of increasing the number of lags increases gradually.
Fifth, the parameters of CARR (1,1) model for maximum likelihood estimation in the sample period, found in the 5% level of significance, the parameter estimation of T value was significant; after the parameters of CARR (1,1) model after filtering, the range sequence sample period has significant heteroscedasticity parameter; CARR (1,1) model can well fit the volatility of the sample period of the Shanghai and Shenzhen 300 index; there is very strong aggregation fluctuation in the CSI 300 index.
Sixth, show the ability to predict the evaluation index and MZ regression equation, regardless of the realized volatility measure "by which way, the sample period of sample period and non parameter CARR (1,1) model parameters are better than CARR (1,1) model.
Compared with other articles, the innovation of this article is mainly based on the following three aspects:
First, the relationship between range and volatility, combined with the parameters of CARR model and non parametric GARCH model, nonparametric CARR model is proposed for the first time and the uniform convergence under weak conditions estimation method, and the consistency of the estimation method is proved. The CARR model parameters from the field to the non the parameter field is extended to the theoretical innovation in the model and the method of estimation.
Second, for the first time on the parameters of CARR (1,1) model and non parameter CARR (1,1) model simulation. In order to poor sequence and leverage effect can better simulate the financial market and strengthen the demonstration of effective and scientific, this paper selected the data generation process and different disturbance distribution parameters of CARR (1,1) model and non parameter CARR (1,1) to evaluate the simulation and prediction ability of the model, according to the simulation parameters of CARR (1,1) fitting ability is better than the parameters of the CARR model (1,1) model can better fit the actual volatility sequence. This part is the non parameter CARR (1,1) model is applied to the financial market lay a good theoretical basis for the empirical research.
Third, for the first time the parameters of CARR (1,1) model is applied to the Shanghai and Shenzhen 300 index range in the sequence of empirical research. In this paper, the Shanghai and Shenzhen 300 index range sequence is divided into two parts of the sample period and the sample period, the parameters of CARR (1,1) model and non parameter CARR (1,1) model is applied to China's Shanghai and Shenzhen 300 index range in the sequence analysis of basic statistical characteristics, model estimation and prediction ability evaluation, on the one hand that the Shanghai and Shenzhen 300 index range sequence is positively biased, aggregated distribution expansion and fluctuation phenomenon; on the other hand, based on the parameters of CARR (1,1) model and non parametric model to evaluate CARR (1,1) the prediction ability of the sample period and sample period and MZ regression, found that the parameters of CARR (1,1) prediction ability is superior to the parameters of the CARR model (1,1) model can better depict China's Shanghai and Shenzhen 300 index volatility. The part from the practical The results are verified with the angle, and the results are more convincing.
This paper is composed of 2011 National Natural Science Foundation of China project "new order driven product error modeling and Application Research on the market > non negative financial time series (71101118) and the 2009 year of Ministry of education, humanities and social science research youth fund project" emerging market financial order driven the duration of the statistical analysis and application "(09YJC910009) funding to complete.

【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F832.51

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