Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models
研究条件异方差模型中拟极大似然估计量的一致性条件，指出非对称分布下需添加位置参数才能识别，并计算对称情形下添加该参数导致的效率损失。
Virtually all applications of time-varying conditional variance models use a quasimaximum-likelihood estimator (QMLE). Consistency of a QMLE requires an identification condition that the quasi-log-likelihood have a unique maximum at the true conditional mean and relative scale parameters. We show that the identification condition holds for a non-Gaussian QMLE if the conditional mean is identically zero or if a symmetry condition is satisfied. Without symmetry, an additional parameter, for the location of the innovation density, must be added for identification. We calculate the efficiency loss from adding such a parameter under symmetry, when the parameter is not needed. We also show that there is no efficiency loss for the conditional variance parameters of a GARCH process.