本文選題：Copula理論 + 貝葉斯估計(jì)　； 參考：《湖南大學(xué)》2013年碩士論文

【摘要】：隨著我國(guó)對(duì)外經(jīng)濟(jì)貿(mào)易的日漸開(kāi)放，金融衍生產(chǎn)品不斷地引進(jìn)和完善，國(guó)內(nèi)金融市場(chǎng)也日益復(fù)雜和多樣化。處在金融危機(jī)頻發(fā)的時(shí)代，如何采用合理的方法來(lái)度量金融市場(chǎng)的風(fēng)險(xiǎn)則顯得相當(dāng)重要。 Copula理論可以度量變量之間的非線性相關(guān)關(guān)系，并能夠?qū)⑦吘壏植己吐?lián)合分布分開(kāi)來(lái)考慮，故其成為當(dāng)下處理金融風(fēng)險(xiǎn)的一把利器。如何選擇一個(gè)合適的邊緣分布對(duì)于Copula建模起著至關(guān)重要的作用，很多實(shí)證表明GARCH-t模型能夠很好地描述金融時(shí)間序列“尖峰厚尾”的特性，傳統(tǒng)GARCH模型的參數(shù)估計(jì)采用的是極大似然估計(jì)方法，當(dāng)遇到目標(biāo)函數(shù)沒(méi)有極大值時(shí)，傳統(tǒng)方法很難實(shí)現(xiàn)目標(biāo)函數(shù)的數(shù)值最優(yōu)化。 貝葉斯估計(jì)是建立在貝葉斯理論基礎(chǔ)之上，將待估參數(shù)看成隨機(jī)變量，結(jié)合先驗(yàn)信息和數(shù)據(jù)信息從而得到參數(shù)的后驗(yàn)密度，在此基礎(chǔ)之上做進(jìn)一步的統(tǒng)計(jì)推斷。與傳統(tǒng)方法相比，通常貝葉斯估計(jì)量具有更小的方差或平方誤差，，能夠得到更精確的預(yù)測(cè)結(jié)果，貝葉斯最大后驗(yàn)置信區(qū)間比不考慮參數(shù)先驗(yàn)信息的頻率置信區(qū)間短。將貝葉斯估計(jì)方法應(yīng)用于GARCH模型的參數(shù)估計(jì)，能夠很好地解決傳統(tǒng)估計(jì)中遇到的一系列問(wèn)題，同時(shí)GARCH模型一系列的約束條件也適合用貝葉斯估計(jì)方法。 本文在介紹Copula理論和貝葉斯理論的基礎(chǔ)之上，采用貝葉斯估計(jì)方法來(lái)進(jìn)行時(shí)變Copula-GARCH模型的建立，最后以農(nóng)林、制造、運(yùn)輸、地產(chǎn)和文化五個(gè)指數(shù)作為研究對(duì)象，考察了其常相關(guān)和時(shí)變相關(guān)關(guān)系，并基于Z檢驗(yàn)方法，考察了其變結(jié)構(gòu)情況，研究結(jié)果表明：2011年11月份地產(chǎn)行業(yè)由于受?chē)?guó)家政策限制、庫(kù)存激增及地產(chǎn)商資金緊缺的影響，其與制造指數(shù)、文化指數(shù)的結(jié)構(gòu)發(fā)生了顯著變化。
[Abstract]:With the opening of China's foreign economy and trade, financial derivatives are continuously introduced and perfected, and the domestic financial market is becoming more and more complex and diversified. In the times of frequent financial crisis, it is very important to adopt reasonable methods to measure the risk of financial market. Copula theory can measure the nonlinear correlation between variables, and consider the edge distribution and joint distribution separately. Therefore, it has become a sharp weapon to deal with financial risks. How to choose an appropriate edge distribution plays an important role in Copula modeling. Many empirical results show that GARCH-t model can well describe the characteristics of financial time series "peak and thick tail". The parameter estimation of traditional GARCH model is based on the maximum likelihood estimation method. When the objective function has no maximum value, the traditional method is difficult to realize the numerical optimization of the objective function. The Bayesian estimation is based on Bayesian theory. The parameters to be estimated are regarded as random variables, and the posterior density of the parameters is obtained by combining the prior information with the data information, and further statistical inference is made on this basis. Compared with the traditional methods, Bayesian estimators usually have smaller variance or square error, and can obtain more accurate prediction results. The Bayesian maximum posterior confidence interval is shorter than the frequency confidence interval which does not take into account the prior parameter information. Applying Bayesian estimation method to parameter estimation of GARCH model can solve a series of problems encountered in traditional estimation. At the same time, a series of constraints of GARCH model are also suitable for Bayesian estimation. Based on the introduction of Copula theory and Bayesian theory, Bayesian estimation method is used to establish the time-varying Copula-GARCH model. Five indexes of transportation, real estate and culture were studied as the research object, and the variable structure was investigated based on the Z test method. The results show that the structure of real estate industry and manufacturing index and culture index changed significantly in November 2011 due to the restriction of national policy, the surge of inventory and the shortage of real estate capital.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F830.91;F224;O212.8

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