疫情冲击下基于ARMA-GARCH模型的道琼斯指数收益率及风险分析方法

Dow-Jones Index Return and Risk Analysis Method Based on ARMA-GARCH Model under Epidemic Impact

摘要: 本文使用ARMA-GARCH模型拟合，分析了疫情期间美国股市2019年至2020年部分期间数据。首先对数据进行检验，得出序列不平稳的结论；应用ARMA-GARCH模型，可以有效地拟合出道琼斯指数收益率序列，得到期间的波动率大小，通过图像能直观判断拟合模型后的波动率变化幅度；通过VaR的滚动预测实证也证实了在3月份，股市的投资风险显著上升。可以得出，利用ARMA-GARCH模型进行股市收益率及风险判断是可行的，拟合效果较好。但是，利用ARMA-GARCH模型时应注意：因为收益率序列的自相关与偏自相关图不是典型的时序图，所以从时间序列图中要准确地把握好ARMA模型，否则容易导致ARMA模型拟合存在偏差；GARCH模型可以进一步尝试其他分布的拟合。

Abstract: This paper uses ARMA-GARCH model fitting to analyze the data of US stock market during the epi-demic period from 2019 to 2020. Firstly, we test the data and draw the conclusion that the se-quence is unstable; using ARMA-GARCH model, we can effectively fit the return series of Dow-Jones index, get the volatility during the period, and intuitively judge the variation range of volatility after fitting the model through the image; through the rolling prediction of VaR, it is also confirmed that the investment risk of the stock market increased significantly in March. It can be concluded that it is feasible to use ARMA-GARCH model to judge stock market return and risk, and the fitting effect is good. However, when using ARMA-GARCH model, we should pay attention to: because the autocor-relation and partial autocorrelation diagrams of return series are not typical time series diagrams, we should accurately grasp the ARMA model from the time series diagram, otherwise it is easy to lead to deviation in the fitting of ARMA model; GARCH model can further try to fit other distribu-tions.