GARCH(1,1)模型的稳健估计比较及应用

The Comparison of Robust Estimates for GARCH (1,1) Model and Application of Example

首先阐述了GARCH(1,1)模型稳健估计的构造方法,然后在模型有无异常值扩散效应约束和异常值比例不同的情况下,比较了传统QMLE估计和多种稳健M估计的表现,结果表明:在数据无异常值下,QMLE估计较优;随着异常值比例增加,稳健Andrew估计表现更好;模型施加异常值扩散效应约束对估计有一定改善但不显著.最后选取波动程度不同的两个阶段沪深300指数的收益率,用模型拟合进行了实例比较,在波动程度较大时,Andrew估计效果较优,在波动相对平稳时,LAD估计较优.

This paper firstly introduces the robust estimates for GARCH （1, 1） model, and then on the condition that the model is bounded or not and with different sizes of outliers we make the comparison of the traditional QMLE estimate and several robust M-estimates. The result shows that： 1） without outliers the QMLE performs better; 2） as the size of outliers becomes larger, the robust estimates perform better relatively, especially Andrew- estimate; 3） bounded model performs better but not positively. At last we use the model to fit two periods of return of CSI300 which has different volatility, outcome show that： 1） with higher volatility Andrew-estimate is well-performed while with lower volatility LAD-estimate is recommended.