兰州大学机构库 >数学与统计学院
混合Pair Copula-核估计模型的基金组合密度函数拟合
Alternative TitleThe fitting for fund portfolio density function with Mixed Pair Copula-Kernel Estimation
路聪卿
Thesis Advisor严定琪
2015-05-24
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword核密度估计 GARCH Copula Pair Copula 条件分布 标准藤
Abstract近年来,Pair Copula函数被广泛应用于金融领域,用来分析高维资产组合间的非线性关系。本文构建了混合Pair Copula-核估计模型,用其拟合了基金组合收益率序列的联合概率密度函数。模型采用核密度估计方法估计边际分布,较GARCH模型而言不需要假设残差序列的分布,能够反应更多时间序列的波动特征。实证中,我们以国泰小盘的重仓持股前五名的股票的收益率序列为研究对象,分别用核密度估计和GARCH模型来估计其边际分布,并对结果做了比较,验证了核密度估计模型优于GARCH模型。另外,在Copula函数的基础上,借“藤”结构分解得到了Pair Copula函数,给出了五维Pair Copula函数的分解过程以及严格证明。模型在选择Pair Copula函数的中心元素时,选择与其它序列相关性均较强的股票收益率序列作为中心元素。模型构造了混合Pair Copula函数,在每一层分解选择二元Copula函数时,选择不同的Copula函数,从数据本身出发,用最合适的二元Copula函数来拟合。在边际分布序列的基础上,用混合Pair Copula函数和非混合Pair Copula函数分别估计基金资产组合的联合概率密度分布函数,将其结果进行比较,得出混合PairCopula函数优于非混合Pair Copula函数估计。
Other AbstractIn recent years, functions of Pair Copula are widely used in financial field. It is used to analyze the nonlinear relationship among these assets. This paper constructed a mixed Pair Copula- kernel estimation model, it is used to fit a combined probability density distribution function for the series of fund portfolio's yield rate. The model uses method which is kernel density estimation to estimate the marginal distribution. Compared with GARCH, it doesn't need the assumption for the distribution of residual sequence. So it can reflect more fluctuation characteristics of time series. We choose the stock yield's series who are among the top five in Guotai small caps as the research object in empirical study, use both kernel estimation and GARCH model to estimate the marginal distribution, and compare the result with the two methods. The conclusion that kernel estimation is better than GARCH model is proved. In addition, it gains Pair Copula function according to Vines analyze on the basis of Copula function. The model chooses the stock yield's series who has stronger correlation with other stock yield's series than others as the center element. The model constructs Mixed Pair Copula function, it chooses different Copula function when it chooses two dimension Copula in every tree, uses the best two dimension Copula to fit from the data itself .On the basis of marginal distribution series, it is used to estimate the combined probability density distribution function of the fund portfolio through both mixed Pair Copula function and non hybrid Pair Copula function. Then, compare with the results, we get that mixed Pair Copula function is better than non hybrid Pair Copula function..
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225275
Collection数学与统计学院
Recommended Citation
GB/T 7714
路聪卿. 混合Pair Copula-核估计模型的基金组合密度函数拟合[D]. 兰州. 兰州大学,2015.
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