Persistence and Kurtosis in GARCH and Stochastic Volatility Models
揭示了GARCH和ARSV模型中峰度、波动率冲击持续性与平方序列一阶自相关之间的不同关系，解释了为何两者拟合同一序列时估计的持续性不同，以及为何高斯ARSV模型常适用而GARCH需厚尾分布。
This article shows that the relationship between kurtosis, persistence of shocks to volatility, and first-order autocorrelation of squares is different in GARCH and ARSV models. This difference can explain why, when these models are fitted to the same series, the persistence estimated is usually higher in GARCH than in ARSV models, and, why gaussian ARSV models seem to be adequate, whereas GARCH models often require leptokurtic conditional distributions. We also show that introducing the asymmetric response of volatility to positive and negative returns does not change the conclusions. These results are illustrated with the analysis of daily financial returns.