二元Archimedean Copula函數(shù)選擇的新方法及相關(guān)模型的改進
發(fā)布時間：2018-09-18 09:48
【摘要】：隨著世界貿(mào)易深度不斷地擴大,加強了地區(qū)與地區(qū)、國家與國家之間的經(jīng)濟交流和合作,經(jīng)濟全球化、一體化的趨勢愈加明顯,使得影響經(jīng)濟發(fā)展的因素不再單一。而各個因素之間的關(guān)系變得錯綜復(fù)雜,所以傳統(tǒng)的基于線性相關(guān)分析金融市場風(fēng)險的模型已經(jīng)不再適用于愈加復(fù)雜的經(jīng)濟體系。以往度量金融序列間相關(guān)關(guān)系時,我們習(xí)慣性地假設(shè)它們的邊緣分布為正態(tài)分布或t分布,以此來減少運算量。但是,這樣的假設(shè)時常與金融數(shù)據(jù)具有尖峰厚尾的特征相矛盾。為了化解這一矛盾,Copula理論的出現(xiàn)為分析金融序列相關(guān)性這類問題提供了一條嶄新的思路,Copula函數(shù)的優(yōu)點主要有兩點:一是能夠?qū)⒆兞康倪吘壏植己吐?lián)合分布分開研究,且邊緣分布的設(shè)定也不再局限于正態(tài)分布或t分布這類少數(shù)的幾種概率分布,可以根據(jù)實際情況選擇恰當?shù)姆植?二是由Copula導(dǎo)出的相關(guān)性度量,不僅能描述序列間存在的線性相關(guān)關(guān)系,更能捕捉到非線性、非對稱的相關(guān)關(guān)系,在具體應(yīng)用中更貼近真實性。Archimedean Copula函數(shù)的生成元具有構(gòu)造簡單、計算方便的特性,且作為Copula函數(shù)的一個重要分支,能有效地刻畫金融領(lǐng)域中多元變量間復(fù)雜的非線性的相關(guān)關(guān)系。但實踐經(jīng)驗表明當選擇不同的Archimedean Copula函數(shù)會得到截然不同的結(jié)果。所以,如何選擇恰當?shù)腁rchimedean Copula函數(shù)來刻畫金融數(shù)據(jù)間的相關(guān)關(guān)系就至關(guān)重要。本文以二元Archimedean Copula函數(shù)為研究對象,從Copula分布函數(shù)?tk?出發(fā),構(gòu)造了一個比分布函數(shù)?tk?的非參數(shù)估計量??tk?更有效的估計量?tk?,再根據(jù)?tk?,?tk?兩者間的距離選擇恰當?shù)腁rchimedean Copula函數(shù)。實證分析表明新方法能夠有效的選擇二元Archimedean Copula函數(shù)模型。在度量金融序列間的相關(guān)性時常常會建立會選擇建立Copula-GPD模型和Copula-GARCH-GPD模型,但這兩個模型存在一定的缺陷。Copula-GPD模型沒有考慮序列存在的條件異方差和波動聚集性,且兩個模型都是選擇單個的Copula函數(shù)進行序列間相關(guān)程度的分析,得到的結(jié)果并不全面。本文試著建立了M-Copula-TGARCH-GPD模型,M-Copula是指采用混合Copula來描述序列相關(guān)性,TGARCH是充分考慮金融序列存在的非對稱性,GPD是用極值理論對尾部進行擬合。實證分析表明M-Copula-TGARCH-GPD模型能更好的體現(xiàn)金融序列間的相關(guān)性。
[Abstract]:With the expansion of the depth of world trade, the economic exchange and cooperation between regions, countries and countries, the trend of economic globalization and integration is becoming more and more obvious, which makes the factors affecting economic development no longer single. The relationship between various factors becomes complicated, so the traditional model based on linear correlation analysis of financial market risk is no longer suitable for increasingly complex economic systems. In the past, when we measured the correlation between financial sequences, we used to assume that their edge distribution is normal distribution or t distribution, so as to reduce the amount of computation. However, such assumptions are often contradicted by the peak and thick tail characteristics of financial data. In order to resolve this contradiction, the emergence of Copula theory provides a new way of thinking for the analysis of financial sequence correlation. The advantages of Copula function are as follows: first, it is possible to study the marginal distribution and joint distribution of variables separately. Moreover, the setting of edge distribution is no longer limited to a few probability distributions such as normal distribution or t distribution, and the proper distribution can be selected according to the actual situation. Not only can the linear correlation between sequences be described, but also the nonlinear and asymmetric correlation can be captured. In practical applications, the generator of the real. Archimedean Copula function has the characteristics of simple construction and convenient calculation. As an important branch of Copula function, it can effectively depict the complex nonlinear correlation among multivariate variables in the field of finance. But practical experience shows that when different Archimedean Copula functions are selected, the results are very different. Therefore, how to choose the appropriate Archimedean Copula function to describe the correlation between financial data is very important. In this paper, the binary Archimedean Copula function is taken as the research object, and the Copula distribution function is used as the object of study. A specific distribution function is constructed. The nonparametric estimator tk? A more effective estimate will be based on the TKM? The distance between the two select the appropriate Archimedean Copula function. Empirical analysis shows that the new method can effectively select the binary Archimedean Copula function model. When we measure the correlation between financial sequences, we often choose to establish Copula-GPD model and Copula-GARCH-GPD model, but the two models have some defects. Copula-GPD model does not take into account the conditional heteroscedasticity and volatility aggregation. Both models select a single Copula function to analyze the correlation between sequences, and the results are not comprehensive. This paper attempts to establish a M-Copula-TGARCH-GPD model in which mixed Copula is used to describe the sequence correlation. TGARCH is an asymmetric M-Copula-TGARCH-GPD model which considers the existence of financial sequences. The extreme value theory is used to fit the tail. Empirical analysis shows that M-Copula-TGARCH-GPD model can better reflect the correlation between financial sequences.
【學(xué)位授予單位】：西華師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：F224
[Abstract]:With the expansion of the depth of world trade, the economic exchange and cooperation between regions, countries and countries, the trend of economic globalization and integration is becoming more and more obvious, which makes the factors affecting economic development no longer single. The relationship between various factors becomes complicated, so the traditional model based on linear correlation analysis of financial market risk is no longer suitable for increasingly complex economic systems. In the past, when we measured the correlation between financial sequences, we used to assume that their edge distribution is normal distribution or t distribution, so as to reduce the amount of computation. However, such assumptions are often contradicted by the peak and thick tail characteristics of financial data. In order to resolve this contradiction, the emergence of Copula theory provides a new way of thinking for the analysis of financial sequence correlation. The advantages of Copula function are as follows: first, it is possible to study the marginal distribution and joint distribution of variables separately. Moreover, the setting of edge distribution is no longer limited to a few probability distributions such as normal distribution or t distribution, and the proper distribution can be selected according to the actual situation. Not only can the linear correlation between sequences be described, but also the nonlinear and asymmetric correlation can be captured. In practical applications, the generator of the real. Archimedean Copula function has the characteristics of simple construction and convenient calculation. As an important branch of Copula function, it can effectively depict the complex nonlinear correlation among multivariate variables in the field of finance. But practical experience shows that when different Archimedean Copula functions are selected, the results are very different. Therefore, how to choose the appropriate Archimedean Copula function to describe the correlation between financial data is very important. In this paper, the binary Archimedean Copula function is taken as the research object, and the Copula distribution function is used as the object of study. A specific distribution function is constructed. The nonparametric estimator tk? A more effective estimate will be based on the TKM? The distance between the two select the appropriate Archimedean Copula function. Empirical analysis shows that the new method can effectively select the binary Archimedean Copula function model. When we measure the correlation between financial sequences, we often choose to establish Copula-GPD model and Copula-GARCH-GPD model, but the two models have some defects. Copula-GPD model does not take into account the conditional heteroscedasticity and volatility aggregation. Both models select a single Copula function to analyze the correlation between sequences, and the results are not comprehensive. This paper attempts to establish a M-Copula-TGARCH-GPD model in which mixed Copula is used to describe the sequence correlation. TGARCH is an asymmetric M-Copula-TGARCH-GPD model which considers the existence of financial sequences. The extreme value theory is used to fit the tail. Empirical analysis shows that M-Copula-TGARCH-GPD model can better reflect the correlation between financial sequences.
【學(xué)位授予單位】：西華師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：F224
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