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波动性是当今金融市场基本的性质,它与股票市场的风险直接相关,可以比较简单有效地对股票市场进行度量。本文通过运用R语言软件建立了GARCH(1,1)模型、TGARCH(1,1)模型和EGARCH(1,1)模型,对德国DAX指数收益率进行时间序列化,并对其进行实证分析。结果表明,德国DAX指数收益率序列存在着非正态分布性、尖峰厚尾性、聚集性、非对称性等特征,并存在着杠杆效应。并运用R语言软件对残差服从正态分布、t分布及GED分布的同一模型进行不同标准程度的对比。实证结果显示,同一分布的前提下,EGARCH模型比GARCH模型能更好地反应股市非对称性的存在,TGARCH模型又进一步深化,发现了杠杆效应。而对于同一种模型,残差服从GED分布的模型的拟合优度优于残差服从t分布的模型,优于残差服从正态分布的模型。
Volatility is the basic nature of today’s financial markets. It is directly related to the risk of the stock market and can measure the stock market relatively simply and effectively. In this paper, the GARCH (1,1) model, the TGARCH (1,1) model and the EGARCH (1,1) model are established by using R language software to time serialize the yield of German DAX and make an empirical analysis. The result shows that the German DAX returns have non-normal distribution, peak-tail-tail, aggregation and asymmetry, and have the leverage effect. And using R language software to compare the residuals under the same standard of normal distribution, t distribution and GED distribution. The empirical results show that, under the same distribution, the EGARCH model can better reflect the existence of asymmetry than the GARCH model, and the TGARCH model further deepens and finds the leverage effect. For the same model, the goodness-of-fit of the model with residuals subject to GED distribution is better than the model with residuals subject to t distribution, which is better than the model with residuals subject to normal distribution.