本文選題：Copula函數(shù)　切入點(diǎn)：高頻金融數(shù)據(jù)　出處：《電子科技大學(xué)》2013年碩士論文　論文類型：學(xué)位論文

【摘要】：掌握金融變量間的相依結(jié)構(gòu)是研究金融體系的運(yùn)作模式，提高投資策略準(zhǔn)確率的基礎(chǔ)和關(guān)鍵所在。Copula函數(shù)具有傳統(tǒng)相關(guān)性分析方法不具備的刻畫(huà)非線性、非對(duì)稱相依結(jié)構(gòu)的能力，尤其是在刻畫(huà)尾部相關(guān)性的能力方面具有明顯的優(yōu)勢(shì)，恰恰符合了研究者對(duì)金融變量相依結(jié)構(gòu)分析的需求。 論文從Copula函數(shù)的定義、主要性質(zhì)、種類以及相應(yīng)的相關(guān)性測(cè)度等方面對(duì)Copula理論做了系統(tǒng)的介紹，并梳理和總結(jié)了Copula模型的建立方法和步驟，包括邊緣分布的確定方法，參數(shù)估計(jì)方法，Copula模型的選擇和模型擬合優(yōu)度評(píng)價(jià)，著重研究了Copula函數(shù)的參數(shù)估計(jì)方法，討論了精確極大似然估計(jì)（EML估計(jì)）、分步估計(jì)（IFM估計(jì)）、基于樣本經(jīng)驗(yàn)分布函數(shù)的CML估計(jì)、基于核密度估計(jì)方法的MLK方法以及GenestRivest估計(jì)法，通過(guò)分析和蒙特卡洛模擬給出了它們的適用條件，并得到結(jié)論：當(dāng)樣本邊緣分布難以確定，或者邊緣分布擬合效果不好的時(shí)候，MLK估計(jì)是最佳參數(shù)估計(jì)方法。 將Copula理論應(yīng)用到高頻金融數(shù)據(jù)的相依結(jié)構(gòu)分析中。根據(jù)高頻數(shù)據(jù)的特點(diǎn)，構(gòu)造了結(jié)合BP神經(jīng)網(wǎng)絡(luò)擬合和Copula函數(shù)的新模型，并實(shí)證了該模型能夠比較有效地刻畫(huà)股指期貨每分鐘絕對(duì)收益率和成交量的相依結(jié)構(gòu)。首先采用BP神經(jīng)網(wǎng)絡(luò)方法擬合并消除日歷效應(yīng)，再用核密度估計(jì)方法來(lái)確定邊緣分布，并根據(jù)邊緣分布的頻率直方圖，分別選取Gumbel Copula函數(shù)和混合阿基米德Copula函數(shù)對(duì)其進(jìn)行擬合，最后利用多種相依性測(cè)度來(lái)評(píng)價(jià)模型擬合的效果。結(jié)果表明：相關(guān)參數(shù)為(?)=1.5421的Gumbel Copula模型很好的描述和刻畫(huà)了股指期貨每分鐘絕對(duì)收益率和成交量之間的相依結(jié)構(gòu)，捕捉到了兩者之間明顯的上尾相關(guān)性和下尾漸近獨(dú)立性，并從投資行為學(xué)上進(jìn)行解釋：當(dāng)市場(chǎng)波動(dòng)劇烈時(shí)，即交易會(huì)導(dǎo)致較大的收益或者損失時(shí)，投資者為了獲得收益或者保本，交易欲望就會(huì)增強(qiáng)，導(dǎo)致交易量的上漲，，而當(dāng)市場(chǎng)波動(dòng)很小時(shí)，投資者基于自己對(duì)未來(lái)市場(chǎng)的預(yù)期，會(huì)保持一定的交易量。
[Abstract]:Mastering the dependent structure among financial variables is the basis of studying the operation mode of financial system, improving the accuracy of investment strategy and the key. Copula function has the ability to describe the nonlinear and asymmetric dependent structure that the traditional correlation analysis method does not have. Especially, it has obvious advantages in the ability to depict the tail correlation, which is exactly in line with the researchers' demand for the analysis of the dependent structure of financial variables. This paper systematically introduces the Copula theory from the definition of Copula function, the main properties, the types and the corresponding correlation measures, and summarizes the methods and steps of establishing Copula model, including the method of determining the edge distribution. The method of parameter estimation is the selection of Copula model and the evaluation of model goodness of fit. The parameter estimation method of Copula function is emphatically studied, and the accurate maximum likelihood estimation, step estimation and CML estimation based on sample empirical distribution function are discussed. The MLK method and GenestRivest estimation method based on kernel density estimation method are analyzed and Monte Carlo simulations are used to give their applicable conditions, and the conclusion is drawn: when the sample edge distribution is difficult to determine, Or MLK estimation is the best parameter estimation method when the fitting effect of edge distribution is not good. The Copula theory is applied to the dependent structure analysis of high frequency financial data. According to the characteristics of high frequency data, a new model combining BP neural network fitting and Copula function is constructed. The model is proved to be able to describe the dependent structure of absolute yield per minute and turnover of stock index futures effectively. Firstly, BP neural network method is used to merge to eliminate calendar effect, and then the kernel density estimation method is used to determine the edge distribution. According to the frequency histogram of the edge distribution, the Gumbel Copula function and the mixed Archimedes Copula function are selected to fit them respectively. Finally, a variety of dependency measures are used to evaluate the effect of the model fitting. The Gumbel Copula model of Gui 1.5421 well describes and depicts the dependent structure between the absolute yield per minute and the trading volume of stock index futures, and captures the obvious correlation between the upper tail and the tail and the asymptotic independence of the lower tail. And explain from the view of investment behavior: when the market fluctuates violently, that is, when the trading will lead to a large profit or loss, the investor's desire to trade will increase in order to obtain the income or to keep the capital, which will lead to the increase of the trading volume. When the market volatility is very small, investors based on their future market expectations, will maintain a certain volume of trading.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F224;F830.91

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