Score Tests for Hyperbolic GARCH Models
重新解读了双曲GARCH模型，构建了简化得分检验以检测波动率中的双曲衰减现象，并推导了检验统计量的渐近性质，通过蒙特卡洛模拟和实际数据验证了其有效性。
Davidson (2004) recently proposed the hyperbolic GARCH model to capture the phenomenon of longrange dependence in volatility, with the extent of such dependence measured by the geometric or hyperbolic decay of the coefficients in an ARCH(∞) model. In this article, we reinterpret the hyperbolic GARCH model by building a link with the common GARCH model, and construct a simplified score test to check the presence of the hyperbolic decay. We derive the asymptotic of the test statistic under the null hypothesis and the local alternatives.We conductMonte Carlo simulation experiments to study the performance of this test, and report an illustration on two log return sequences. This article has supplementary material online. © 2011 American Statistical Association.