文档介绍：河北大学
硕士学位论文
基于日历效应和厚尾分布的收益率波动性分析
姓名:刘莎莎
申请学位级别:硕士
专业:统计学
指导教师:陈志国
20100501
摘要
摘要
股票收益率波动性对于 VaR(Value-at-Risk)的预测和股市投资者的投资等有重要
的意义,因此引起了众多学者的关注。当今刻画股票收益率波动性的模型总体上来说有
两大类:一类是 ARCH(自回归条件异方差)模型簇,一类是 SV(随机波动)模型,本
文采用其中的 ARCH 模型簇(包括GARCH,TARCH,EGARCH,PARCH 几个模型)进行建模分析。
本文在充分考虑到日历效应对均值方程的影响和不同残差分布假设对方差方程的影响
后,用 ARCH 模型簇对最能反映中国股市波动情况的上证综指对数收益率的波动进行建
模。经过实证分析,收益率不服从正态分布,从统计特征图和 QQ 图可以看出收益率的
分布较正态分布有更厚的尾;通过在均值方程中加入星期虚拟变量可以看出中国的股票
市场存在日历效应,星期一和星期三的收益率要高于星期二、星期四和星期五的收益率;
在充分考虑到影响均值方程的日历效应后,基于残差正态分布假定的方差方程存在杠杆
效应,而基于残差 t 分布的方差方程不存在明显的杠杆效应,即反映非对称性效应的系
数不是统计显著的,这说明以往学者得出的中国股市存在杠杆效应的结论可能是由于均
值方程残差分布形式的假定不精确所造成的;从本文所选择的模型来看,根据AIC 和 SC
信息准则,无论是 ARCH 模型簇中的哪个模型,基于 t 分布的方差方程都比基于正态分
布的方差方程的拟合效果要好。

关键词日历效应 t-分布 ARCH 模型簇杠杆效应

I
Abstract
Abstract
The volatility of stock returns has important significance to the forecast of VaR and the
investing of the investors. Therefore, it attracts the attentions of many scholars. At present,
there are two kinds of models which can be used to describe the volatility of stock returns:
one is ARCH (autoregressive conditional heteroscedasticity) models and another is SV
(stochastic volatility) model. In this paper, we only use the ARCH models to characterize the
volatility of stock returns. After considering calendar’s effects on the mean equation and
different distribution assumptions of residuals’s effect on the variance equation fully, the
author uses several ARCH models to analyze the volatility of the returns of shanghai
composite which can most greatly reflect the stock market’s volatility of China. After the
demonstration analysis, we know that the return yield does not obey the normal distribution,
and from the statistical characteristic pictures and QQ we see that the distribution of return
yields with a thicker tail which is obviously larger than the normal-distribution. We add week
virtual variables to mean equation and find the calendar effect exist in China’s stock markets: