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  本文選題：Copula函數(shù) + GARCH模型��； 參考：《華中科技大學(xué)》2012年碩士論文

【摘要】：線性相關(guān)系數(shù)和Granger因果關(guān)系分析是最傳統(tǒng)的相關(guān)性分析方法，而這兩種方法只適合于有線性相關(guān)關(guān)系的變量，大多數(shù)金融變量之間都呈現(xiàn)出非線性關(guān)系，用線性相關(guān)系數(shù)來描述它們之間的相關(guān)性會存在一些誤導(dǎo)。Copula函數(shù)是將若干個邊緣分布連接起來形成聯(lián)合分布的連接函數(shù)，由它推導(dǎo)出來的相關(guān)性測度在非線性單調(diào)增變換下保持不變，能夠克服線性相關(guān)系數(shù)使用中的局限性，在描述金融變量間的相關(guān)性及相關(guān)結(jié)構(gòu)方面有較多的優(yōu)勢。 本文在介紹時間序列和Copula函數(shù)基礎(chǔ)理論的基礎(chǔ)上，選取2009年9月2日到2011年12月16日的國際黃金價格和美元指數(shù)作為樣本，通過建立Copula模型來描述黃金價格和美元指數(shù)之間的相關(guān)性。模型的建立分兩步完成：首先，確定邊緣分布，它描述了黃金價格和美元指數(shù)收益率的分布特征；其次，選取適合的Copula函數(shù)，它描述的是兩者之間的相關(guān)結(jié)構(gòu)。本文采用金融時間序列模型來確定邊緣分布，通過Eviews6.0軟件對樣本數(shù)據(jù)進(jìn)行分析并做適當(dāng)?shù)奶幚�，選用GARCH模型來估計(jì)黃金價格和美元指數(shù)收益率的邊緣分布，并用分位數(shù)-分位數(shù)圖評價了模型的擬合效果；對于Copula函數(shù)的選擇，本文從二元正態(tài)Copula、二元t-Copula、GumbelCopula、ClaytonCopula及FrankCopula這五種Copula函數(shù)入手，通過估計(jì)線性相關(guān)參數(shù)、求相關(guān)性測度、繪制Copula函數(shù)的分布函數(shù)和密度函數(shù)，舍棄不適合的Copula函數(shù)，選擇用二元正態(tài)Copula、二元t-Copula和FrankCopula來描述黃金價格和美元指數(shù)的相關(guān)結(jié)構(gòu)，最后通過引入經(jīng)驗(yàn)Copula函數(shù)，得出二元t-Copula擬合效果最好的結(jié)論。 本文最終確定用t-Copula-GARCH模型來模擬黃金價格和美元指數(shù)之間的相關(guān)性及相關(guān)結(jié)構(gòu)，并給出了結(jié)論所有具有的理論和現(xiàn)實(shí)意義，為投資者進(jìn)行投資分析提供了良好的建議，，提醒投資者在投資黃金時應(yīng)特別留意美元指數(shù)的急劇變化，以規(guī)避風(fēng)險。
[Abstract]:Linear correlation coefficient and Granger causality analysis are the most traditional correlation analysis methods. It is misleading to use linear correlation coefficient to describe the correlation between them. Copula function is a join function that connects several edge distributions together to form a joint distribution. The correlation measure derived from it is invariant under the condition of nonlinear monotone increasing transformation, which can overcome the limitation of the use of linear correlation coefficient, and has many advantages in describing the correlation between financial variables and related structures. Based on the introduction of time series and the basic theory of Copula function, this paper selects the international gold price and dollar index from September 2, 2009 to December 16, 2011 as samples. Copula model is established to describe the correlation between gold price and dollar index. The establishment of the model is divided into two steps: first, the marginal distribution is determined, which describes the distribution characteristics of gold price and the dollar index yield; secondly, the appropriate Copula function is selected, which describes the correlation structure between the two. In this paper, the financial time series model is used to determine the edge distribution, the Eviews6.0 software is used to analyze and process the sample data, and the GARCH model is used to estimate the marginal distribution of gold price and dollar index yield. The fitting effect of the model is evaluated by quartile-quartile graph. For the selection of Copula function, this paper starts with five Copula functions, namely binary normal Copula, binary t-Copula GumbelCopula Clayton Copula and FrankCopula, and obtains the correlation measure by estimating the linear correlation parameters. The distribution function and density function of Copula function are drawn, and the unsuitable Copula function is given up. The binary normal Copula, binary t-Copula and FrankCopula are chosen to describe the related structure of gold price and dollar index. Finally, the empirical Copula function is introduced. The conclusion that binary t-Copula fitting is the best. In this paper, t-Copula-GARCH model is used to simulate the correlation and structure between gold price and dollar index, and the conclusion is all theoretical and practical significance, which provides a good suggestion for investors to carry out investment analysis. Investors are reminded to pay special attention to the sharp changes in the dollar index when investing in gold in order to avoid risk.
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F831.5;F224

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本文編號：1944952