基于馬爾科夫轉(zhuǎn)換ARCH模型的上證綜指波動率研究
發(fā)布時間：2019-03-27 06:46
【摘要】：作為經(jīng)濟走勢的晴雨表，我國的股票市場在經(jīng)過了20多年的發(fā)展，積累了較大的泡沫成分，體現(xiàn)出一定程度的市場波動性，故度量、刻畫分析波動的特征有著重要的意義。本文以上證綜指收益率序列為例，對于這類復雜的金融數(shù)據(jù)，采用極大似然估計方法得出簡單的GARCH族模型無法刻畫出波動序列的尖峰厚尾性，聚集性，長期記憶性以及杠桿性等諸多特征。 因此，為了能夠更好的刻畫出波動特征，本文首先嘗試利用R/S分析法，，假設(shè)殘差分別在正態(tài)分布、t分布、GED分布及SKT分布下，使用“滾動時間窗”的方法對波動率進行預測，并采用ARFIMA(p,d,q)-EGARCH(m,n)-M模型對收益率序列進行了實證分析。實證結(jié)果表明：上證收益率序列存在長記憶性；基于SKT分布條件下ARFIMA(2,1)-EGARCH(1,1)-M模型能夠較好的處理序列尖峰厚尾和聚集等特征并且較其他分布條件下具備較強的預測精度。 隨后在GARCH族模型的基礎(chǔ)上，結(jié)合了馬爾科夫機制轉(zhuǎn)換的狀態(tài)空間模型對其進行了擴展，文中討論了三狀態(tài)的MS-ARCH(3)模型，并且采用MCMC方法對參數(shù)進行估計，將采樣Metropolis-Hasting取樣法嵌套于Gibbs取樣法中的方法，對參數(shù)進行取樣。研究發(fā)現(xiàn)：MS-ARCH模型比GARCH族模型在刻畫波動聚集特征方面表現(xiàn)的更優(yōu)異，尤其是能夠處理GARCH族所不能刻畫的結(jié)構(gòu)突變的特點，MS-ARCH優(yōu)勢還體現(xiàn)實際應(yīng)用方面，如危機預警的作用。此外，還建議投資者把握好高波動時的獲益機會，但是當高波動狀態(tài)開始大量聚集的時候，就要提高警惕，謹防危機帶來的損失。
[Abstract]:As a barometer of economic trend, after more than 20 years of development, China's stock market has accumulated a large bubble component, reflecting a certain degree of market volatility, so it is of great significance to measure and depict and analyze the characteristics of volatility. This paper takes the return series of Shanghai Composite Index as an example. For this kind of complex financial data, using the maximum likelihood estimation method, the simple GARCH family model can not depict the peak-thick-tail property and aggregation of the volatility series, and the method of maximum likelihood estimation is used to obtain a simple GARCH family model. Long-term memory and leverage and many other characteristics. Therefore, in order to better characterize the wave characteristics, this paper first attempts to use the RES analysis to assume that the residuals are under the normal distribution, t distribution, GED distribution and SKT distribution, respectively, and that the residual error is in the normal distribution, t distribution, SKT distribution and so on. ARFIMA (p, d, Q)-EGARCH (m, n)-M model is used to predict the volatility using the "rolling time window" method, and the empirical analysis of the yield series is carried out. The empirical results show that there is a long memory in the return series of Shanghai Stock Exchange. Based on the SKT distribution, the ARFIMA (2,1)-EGARCH (1,1)-M model can better deal with the characteristics of peak, thick tail and aggregation of the sequence, and has better prediction accuracy than other distribution conditions. Then on the basis of GARCH family model, it is extended by the state space model of Markov mechanism transformation. The three-state MS-ARCH (3) model is discussed in this paper, and the MCMC method is used to estimate the parameters. The sampling Metropolis-Hasting sampling method is nested in the Gibbs sampling method, and the parameters are sampled. It is found that the MS-ARCH model performs better than the GARCH model in describing the characteristics of wave aggregation, especially in dealing with the characteristics of structural changes that can not be characterized by the GARCH family. The advantages of MS-ARCH are also reflected in the practical application, and the advantages of GARCH model are better than those of the GARCH family. Such as the role of crisis warning. In addition, investors are advised to take advantage of high volatility, but when high volatility begins to gather in large numbers, be vigilant and beware of the losses caused by the crisis.
【學位授予單位】：華東交通大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：F224;F832.51
本文編號：2447954
[Abstract]:As a barometer of economic trend, after more than 20 years of development, China's stock market has accumulated a large bubble component, reflecting a certain degree of market volatility, so it is of great significance to measure and depict and analyze the characteristics of volatility. This paper takes the return series of Shanghai Composite Index as an example. For this kind of complex financial data, using the maximum likelihood estimation method, the simple GARCH family model can not depict the peak-thick-tail property and aggregation of the volatility series, and the method of maximum likelihood estimation is used to obtain a simple GARCH family model. Long-term memory and leverage and many other characteristics. Therefore, in order to better characterize the wave characteristics, this paper first attempts to use the RES analysis to assume that the residuals are under the normal distribution, t distribution, GED distribution and SKT distribution, respectively, and that the residual error is in the normal distribution, t distribution, SKT distribution and so on. ARFIMA (p, d, Q)-EGARCH (m, n)-M model is used to predict the volatility using the "rolling time window" method, and the empirical analysis of the yield series is carried out. The empirical results show that there is a long memory in the return series of Shanghai Stock Exchange. Based on the SKT distribution, the ARFIMA (2,1)-EGARCH (1,1)-M model can better deal with the characteristics of peak, thick tail and aggregation of the sequence, and has better prediction accuracy than other distribution conditions. Then on the basis of GARCH family model, it is extended by the state space model of Markov mechanism transformation. The three-state MS-ARCH (3) model is discussed in this paper, and the MCMC method is used to estimate the parameters. The sampling Metropolis-Hasting sampling method is nested in the Gibbs sampling method, and the parameters are sampled. It is found that the MS-ARCH model performs better than the GARCH model in describing the characteristics of wave aggregation, especially in dealing with the characteristics of structural changes that can not be characterized by the GARCH family. The advantages of MS-ARCH are also reflected in the practical application, and the advantages of GARCH model are better than those of the GARCH family. Such as the role of crisis warning. In addition, investors are advised to take advantage of high volatility, but when high volatility begins to gather in large numbers, be vigilant and beware of the losses caused by the crisis.
【學位授予單位】：華東交通大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：F224;F832.51
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