基于變換核密度估計的半?yún)?shù)GARCH模型研究
發(fā)布時間：2018-10-23 08:07
【摘要】：對金融資產(chǎn)波動性的建模是金融時間序列分析的重要內(nèi)容,其對于資產(chǎn)定價、金融風(fēng)險管理以及市場微觀結(jié)構(gòu)分析都有著重要的意義。金融資產(chǎn)的波動通常表現(xiàn)出聚集性和長記憶性,且正的收益率和負(fù)的收益率會對波動率產(chǎn)生非對稱的影響,即所謂的“杠桿效應(yīng)”。GARCH模型是最為常用的描述金融資產(chǎn)波動特征的時間序列模型。 對于傳統(tǒng)的參數(shù)化GARCH模型,通過設(shè)定收益率的條件分布為某一特定的參數(shù)分布,繼而可由極大似然估計法得到模型的參數(shù)估計,其中最為常用的是基于條件正態(tài)假設(shè)的偽極大似然估計(QMLE)。但大量的文獻(xiàn)研究表明,收益率的分布通常具有尖峰、厚尾及有偏的特點,其條件分布往往也非常不均勻,并不符合正態(tài)性假定。雖然在滿足一定的正則條件下,QMLE是漸近相合的,但其在效率上的損失也是不容忽視的。此外,基于特定分布假設(shè)下的參數(shù)化模型往往具有較高的模型誤設(shè)風(fēng)險。為此,一些學(xué)者將非參數(shù)方法與參數(shù)化的GARCH設(shè)定相結(jié)合,建立了不依賴于條件分布假設(shè)的半?yún)?shù)GARCH模型,以期提高參數(shù)估計的相對效率以及模型的精準(zhǔn)度。但傳統(tǒng)的非參數(shù)方法并不能很好地估計收益率的條件分布密度,尤其無法捕捉厚尾特征。 針對上述問題,本文借鑒變換核密度估計的思想,提出了一種廣義Logistic變換,并對變換后的樣本應(yīng)用Beta核密度估計以克服“邊界偏差”問題。模擬試驗表明,該方法顯著提高了對尖峰厚尾分布密度的估計精度。繼而將該方法與參數(shù)化的GARCH設(shè)定相結(jié)合,構(gòu)建了一種新的半?yún)?shù)GARCH模型。該模型具有兩個優(yōu)點：第一,基于變換核密度估計可更加準(zhǔn)確地估計收益率的條件分布；第二,通過迭代提高了參數(shù)估計的穩(wěn)健性。模擬試驗表明,較之偽極大似然估計法和基于離散最大懲罰似然估計的半?yún)?shù)方法,該方法大大提高了參數(shù)估計的相對效率。對滬深300指數(shù)的實證研究驗證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.
【學(xué)位授予單位】：中國科學(xué)技術(shù)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F224;F830.91
本文編號：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.
【學(xué)位授予單位】：中國科學(xué)技術(shù)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F224;F830.91
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