基于变换核密度估计的半参数GARCH模型研究
发布时间：2018-10-23 08:07
【摘要】：对金融资产波动性的建模是金融时间序列分析的重要内容,其对于资产定价、金融风险管理以及市场微观结构分析都有着重要的意义。金融资产的波动通常表现出聚集性和长记忆性,且正的收益率和负的收益率会对波动率产生非对称的影响,即所谓的“杠杆效应”。GARCH模型是最为常用的描述金融资产波动特征的时间序列模型。 对于传统的参数化GARCH模型,通过设定收益率的条件分布为某一特定的参数分布,继而可由极大似然估计法得到模型的参数估计,其中最为常用的是基于条件正态假设的伪极大似然估计(QMLE)。但大量的文献研究表明,收益率的分布通常具有尖峰、厚尾及有偏的特点,其条件分布往往也非常不均匀,并不符合正态性假定。虽然在满足一定的正则条件下,QMLE是渐近相合的,但其在效率上的损失也是不容忽视的。此外,基于特定分布假设下的参数化模型往往具有较高的模型误设风险。为此,一些学者将非参数方法与参数化的GARCH设定相结合,建立了不依赖于条件分布假设的半参数GARCH模型,以期提高参数估计的相对效率以及模型的精准度。但传统的非参数方法并不能很好地估计收益率的条件分布密度,尤其无法捕捉厚尾特征。 针对上述问题,本文借鉴变换核密度估计的思想,提出了一种广义Logistic变换,并对变换后的样本应用Beta核密度估计以克服“边界偏差”问题。模拟试验表明,该方法显著提高了对尖峰厚尾分布密度的估计精度。继而将该方法与参数化的GARCH设定相结合,构建了一种新的半参数GARCH模型。该模型具有两个优点：第一,基于变换核密度估计可更加准确地估计收益率的条件分布；第二,通过迭代提高了参数估计的稳健性。模拟试验表明,较之伪极大似然估计法和基于离散最大惩罚似然估计的半参数方法,该方法大大提高了参数估计的相对效率。对沪深300指数的实证研究验证了本文模型的有效性。
[Abstract]:The modeling of financial asset volatility is an important part of financial time series analysis, which is of great significance for asset pricing, financial risk management and market microstructure analysis. The volatility of financial assets usually shows agglomeration and long memory, and the positive and negative returns have an asymmetric effect on volatility. GARCH model is the most commonly used time series model to describe the volatility characteristics of financial assets. For the traditional parameterized GARCH model, the parameter estimation of the model can be obtained by setting the conditional distribution of the return rate as a particular parameter distribution, and then the maximum likelihood estimation method can be used to estimate the parameters of the model. The most commonly used one is pseudo maximum likelihood estimation (QMLE).) based on conditional normal assumption. However, a large number of literature studies show that the distribution of return rate usually has the characteristics of peak, thick tail and bias, and its conditional distribution is often very uneven, which does not accord with the assumption of normality. Although QMLE is asymptotically consistent under certain regular conditions, the loss of its efficiency can not be ignored. In addition, parameterized models based on the assumption of specific distribution often have a high risk of model missetting. For this reason, some scholars have combined the nonparametric method with parameterized GARCH setting to establish a semi-parametric GARCH model which does not depend on the conditional distribution hypothesis, in order to improve the relative efficiency of parameter estimation and the accuracy of the model. But the traditional nonparametric method can not estimate the conditional distribution density of return rate, especially can not capture the feature of thick tail. In view of the above problems, a generalized Logistic transform is proposed based on the idea of kernel density estimation of transformation, and the Beta kernel density estimation is applied to the transformed samples to overcome the "boundary deviation" problem. The simulation results show that this method can improve the estimation accuracy of the distribution density of the thick tail of the peak. Then, a new semi-parametric GARCH model is constructed by combining the method with parameterized GARCH setting. The model has two advantages: first, the conditional distribution of the return rate can be estimated more accurately based on the transform kernel density estimation; second, the robustness of the parameter estimation is improved by iteration. Simulation results show that compared with pseudo-maximum likelihood estimation and semi-parametric estimation based on discrete maximum penalty likelihood estimation, the relative efficiency of parameter estimation is greatly improved. The validity of this model is verified by the empirical research on Shanghai and Shenzhen 300 index.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.91
本文编号：2288621
[Abstract]:The modeling of financial asset volatility is an important part of financial time series analysis, which is of great significance for asset pricing, financial risk management and market microstructure analysis. The volatility of financial assets usually shows agglomeration and long memory, and the positive and negative returns have an asymmetric effect on volatility. GARCH model is the most commonly used time series model to describe the volatility characteristics of financial assets. For the traditional parameterized GARCH model, the parameter estimation of the model can be obtained by setting the conditional distribution of the return rate as a particular parameter distribution, and then the maximum likelihood estimation method can be used to estimate the parameters of the model. The most commonly used one is pseudo maximum likelihood estimation (QMLE).) based on conditional normal assumption. However, a large number of literature studies show that the distribution of return rate usually has the characteristics of peak, thick tail and bias, and its conditional distribution is often very uneven, which does not accord with the assumption of normality. Although QMLE is asymptotically consistent under certain regular conditions, the loss of its efficiency can not be ignored. In addition, parameterized models based on the assumption of specific distribution often have a high risk of model missetting. For this reason, some scholars have combined the nonparametric method with parameterized GARCH setting to establish a semi-parametric GARCH model which does not depend on the conditional distribution hypothesis, in order to improve the relative efficiency of parameter estimation and the accuracy of the model. But the traditional nonparametric method can not estimate the conditional distribution density of return rate, especially can not capture the feature of thick tail. In view of the above problems, a generalized Logistic transform is proposed based on the idea of kernel density estimation of transformation, and the Beta kernel density estimation is applied to the transformed samples to overcome the "boundary deviation" problem. The simulation results show that this method can improve the estimation accuracy of the distribution density of the thick tail of the peak. Then, a new semi-parametric GARCH model is constructed by combining the method with parameterized GARCH setting. The model has two advantages: first, the conditional distribution of the return rate can be estimated more accurately based on the transform kernel density estimation; second, the robustness of the parameter estimation is improved by iteration. Simulation results show that compared with pseudo-maximum likelihood estimation and semi-parametric estimation based on discrete maximum penalty likelihood estimation, the relative efficiency of parameter estimation is greatly improved. The validity of this model is verified by the empirical research on Shanghai and Shenzhen 300 index.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.91
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