Influence Diagnostics in Generalized Autoregressive Conditional Heteroscedasticity Processes
在GARCH模型中提出基于曲率和斜率的局部影响诊断方法，通过蒙特卡洛研究确定显著性基准，并用纽约证交所数据验证其有效性，尤其能发现斜率法遗漏的异常点。
Influence diagnostics have become important tools for statistical analysis since the seminal work by Cook. In this article we present a curvature-based directional diagnostic, set up based on the slope-based diagnostic to assess the local influence of minor perturbations on influence graph in a regression model. Using both slope- and curvature-based diagnostics, we examine local influence in the generalized autoregressive conditional heteroscedasticity (GARCH) model under two perturbation schemes that involve model perturbation and data perturbation. We present a Monte Carlo study to obtain the approximate benchmark for determining the significance of a directional diagnostic, as well as the threshold for locating influential observations. An empirical study involving GARCH modeling of the continuously compounded daily return of the New York Stock Exchange composite index illustrates the effectiveness of the proposed diagnostics. The empirical study also shows that the curvature-based diagnostic can find a cluster of additive shocks that cannot be discovered by the slope-based diagnostic. Because observations may have different effects on the influence graph under different perturbation schemes, and both the slope-based and the curvature-based diagnostics are useful for assessing local influence (especially in GARCH models), it is advisable to assess local influence under different perturbation schemes through both diagnostics.