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在受控过程中,经常出现自相关性和波动簇聚性并存的特征,这违反了常规控制图的独立性假定。一般情况下采用的修正方法都是运用ARMA模型表示质量过程,用自相关模型及其残差图解决自相关问题。本文尝试运用GARCH类模型及其残差控制图来解决控制过程中出现的波动簇聚问题。并以美国股票市场中的IBM股票为例进行简单的实证分析。通过对其日收益率序列进行建模,从而评判该类型残差控制图的有效性。结果表明:控制图在含有相关性和波动性的受控过程中同样有效,其预警作用也比较显著。
In the controlled process, the characteristics of coexistence of self-correlation and fluctuation clustering often appear, which violates the independence assumption of the conventional control chart. In general, the correction methods adopted are the use of ARMA model to represent the quality process, and the autocorrelation model and its residual graph are used to solve the autocorrelation problem. This paper attempts to use the GARCH class model and its residual control chart to solve the problem of fluctuations in the control process clustering. And take the IBM stock in the U.S. stock market as an example for a simple empirical analysis. Through the modeling of daily return series, the validity of this type of residual control chart can be judged. The results show that the control chart is also valid in controlled process with correlation and volatility, and its warning effect is also significant.