Inference for the tail index of a GARCH(1,1) model and an AR(1) model with ARCH(1) errors
研究了GARCH(1,1)和带ARCH(1)误差的AR(1)模型的尾指数估计，提出用最小绝对偏差估计替代拟极大似然估计，放松了对误差四阶矩有限的要求，并用剖面经验似然法构造置信区间。
For a GARCH(1,1) sequence or an AR(1) model with ARCH(1) errors, one can estimate the tail index by solving an estimating equation with unknown parameters replaced by the quasi maximum likelihood estimation, and a profile empirical likelihood method can be employed to effectively construct a confidence interval for the tail index. However, this requires that the errors of such a model have at least a finite fourth moment. In this article, we show that the finite fourth moment can be relaxed by employing a least absolute deviations estimate for the unknown parameters by noting that the estimating equation for determining the tail index is invariant to a scale transformation of the underlying model.