基于G-ARMA-GARCH族模型的沪深指数日收益率序列模型研究

发布时间：2018-05-17 10:10

  本文选题：上证新综指 + 深证成指　； 参考：《南京大学》2017年硕士论文

【摘要】：在股市的价格变化中,波动率是个十分重要的指标,也是许多国内外学者研究的热点问题。不同发展水平的股票市场中均存在着波动的不对称特征、方差时变特征和簇集特征,而且序列中的负向收益给股票价格带来的波动往往比正向收益来的大,说明股票的价格序列中存在着杠杆效应。与国外发达国家的股市相比,我国沪深股市的起步比较晚,发展还不够成熟,股票市场的监管措施还不那么完善,因此我国离发展成熟的股票市场还有很大差距。本文考虑了我国沪深股市的现状,研究了沪深股市中价格的非对称特征和波动特征,进一步加深了我们对沪深股市波动情况的了解。在我国沪深股市中,上证综指和深证成指是两种主要的指数。本文以上海证券交易所股权分置改革为起点,以深圳证券交易所重新修订深证成指编制方案为终点,综合运用了描述性统计方法和基于G-ARMA-GARCH族模型的实证分析法分别对2006年1月4日至2015年5月19日两种指数日收益率序列的波动情况进行了刻画,并对两种指数进行了对比。最后,根据拟合出的最佳模型分别预测了 2015年5月20日至2015年12月31日两种指数的日收盘价数据。在描述性统计分析中,我们分别讨论了两种指数的正态性、平稳性、异方差性、自相关性和偏自相关性。结果显示上证新综指和深证成指的日收益率序列均是平稳序列,说明可以用ARMA模型进行序列条件均值的初步拟合。同时两种指数的日收益率序列均存在左偏特征和尖峰厚尾特征,说明序列可能存在异方差性,可以用GARCH族模型拟合序列的条件方差。在运用G-ARMA-GARCH族模型进行实证分析的过程中,考虑到当日开盘价与历史收盘价之间可能存在一定的关系,我们在ARMA-GARCH族模型中加入了梯度因子来更好地反映历史数据和隔夜跳空因素对序列波动情况的影响。结果显示GARCH族模型中的EGARCH模型比TGARCH模型更适合拟合上证新综指和深证成指日收益率序列的条件方差,而且在序列的残差项服从GED分布时拟合效果最好。此外,我们发现两种指数的日收益率序列中均存在杠杆效应,且深证成指的杠杆效应更强。同时,深证成指日收益率序列条件方差的波动幅度也比较大,说明深证成指的风险水平更高。经过比较传统的ARMA-GARCH族模型和G-ARMA-GARCH族模型在预测日后收盘价时的精度差异,发现加入梯度因子后的模型预测的精度更高,稳定性也更强。根据描述性统计分析和实证分析,我们可以发现我国沪深股市中还存在许多问题,今后我们需要通过更深入的研究来改善这些问题,以推动我国沪深股市的进一步发展。
[Abstract]:Volatility is a very important index in the price change of stock market, and it is also a hot issue studied by many scholars at home and abroad. In the stock market with different levels of development, there are asymmetric characteristics of volatility, time-varying variance and clustering characteristics, and the negative return in the series often brings more volatility to the stock price than the positive return. It shows that there is a leverage effect in the stock price sequence. Compared with the stock market of the developed countries, the stock market of Shanghai and Shenzhen started relatively late, the development of the stock market is not mature enough, and the supervision measures of the stock market are not so perfect, so there is still a big gap between our country and the mature stock market. This paper considers the present situation of Shanghai and Shenzhen stock markets, studies the asymmetric and fluctuating characteristics of prices in Shanghai and Shenzhen stock markets, and further deepens our understanding of the volatility of Shanghai and Shenzhen stock markets. In Shanghai and Shenzhen stock markets, Shanghai Composite Index and Shenzhen Composite Index are two main indexes. This paper starts with the reform of the split share structure of the Shanghai Stock Exchange, and ends with the Shenzhen Stock Exchange's revision of the Shenzhen Stock Exchange's plan for the compilation of the Shenzhen Stock Exchange's constituent index. In this paper, descriptive statistical method and empirical analysis method based on G-ARMA-GARCH family model are used to characterize the volatility of two kinds of index daily return series from January 4, 2006 to May 19, 2015, and to compare the two indices. Finally, the daily closing price data of the two indices from May 20, 2015 to December 31, 2015 are predicted according to the best fitting model. In descriptive statistical analysis, we discuss the normality, stationarity, heteroscedasticity, autocorrelation and partial autocorrelation of two indices. The results show that the daily yield series of Shanghai New Composite Index and Shenzhen Composite Index are stationary series, which indicates that the ARMA model can be used to preliminarily fit the conditional mean of the sequence. At the same time, the daily returns of the two indices have left bias and sharp peak and thick tail, which indicates that the sequence may have heteroscedasticity, and the conditional variance of the sequence can be fitted by GARCH family model. In the process of empirical analysis using G-ARMA-GARCH family model, considering that there may be a certain relationship between the opening price of the day and the historical closing price, The gradient factor is added to the ARMA-GARCH family model to better reflect the influence of historical data and overnight hopping factors on the fluctuation of the series. The results show that the EGARCH model in the GARCH family model is more suitable than the TGARCH model to fit the conditional variance of the daily return sequence of the Shanghai New Composite Index and the Shenzhen Composite Index, and the best fitting effect is obtained when the residual items of the series are distributed from GED. In addition, we find that there is a leverage effect in the daily yield series of the two indices, and the leverage effect of Shenzhen Composite Index is stronger. At the same time, the volatility of conditional variance in the daily yield series of Shenzhen Composite Index is also large, which indicates that the risk level of Shenzhen Composite Index is higher. By comparing the accuracy difference between the traditional ARMA-GARCH family model and the G-ARMA-GARCH family model in predicting the closing price in the future, it is found that the model with gradient factor has higher accuracy and stronger stability. According to descriptive statistical analysis and empirical analysis, we can find that there are still many problems in China's Shanghai and Shenzhen stock markets. In the future, we need to improve these problems through more in-depth research in order to promote the further development of China's Shanghai and Shenzhen stock markets.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F832.51
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本文编号：1900970