深证综指的ARMA-GARCH模型实证分析

Empirical analysis of the ARMA-GARCH model of the Shenzhen composite index

选取1991-04-03至2020-01-10期间的深证综合指数日收盘价为样本数据,为保证序列的平稳性,先取样本数据的对数再进行一阶差分处理,得到对数日收益率序列,分析其基本统计特征,并验证序列的稳定性、自相关性与ARCH效应,发现深证综合指数对数日收益率序列具有尖峰厚尾性、异方差性以及杠杆效应等特点,最后基于数据特征分析建立了ARMA-GARCH和ARMA-EGARCH两种模型分别对序列进行拟合、描述及分析,运用AIC等模型评价标准,综合对比发现ARMA(1,1)-GARCH(1,1)模型分析深证综指效果更优。

In order to ensure the stability of the series,the logarithm of this data is first sampled and then the first order difference processing is carried out to obtain the log-daily yield sequence,analyze its basic statistical characteristics,and verify its stability,autocorrelation and ARCH effect.It is found that the log-daily yield sequence has the characteristics of spike-thick tail,heteroscedasticity and lever effect.Finally,based on the data feature analysis,ARMA-GARCH and ARMA-EGARCH models are established respectively list fitting,description and analysis,the use of AIC and other model evaluation criteria,comprehensive comparison found that ARMA(1,1)-GARCH(1,1)model analysis is better.