ESTIMATING WEAK GARCH REPRESENTATIONS
论文指出标准GARCH模型对条件矩的强假设常被违背，导致估计不一致，提出用弱GARCH表示（基于误差平方项的ARMA结构）并通过两阶段最小二乘法估计参数，该估计量一致且渐近正态。
The classical definitions of GARCH-type processes rely on strong assumptions on the first two conditional moments. The common practice in empirical studies, however, has been to test for GARCH by detecting serial correlations in the squared regression errors. This can be problematic because such autocorrelation structures are compatible with severe misspecifications of the standard GARCH. Numerous examples are provided in the paper. In consequence, standard (quasi-) maximum likelihood procedures can be inconsistent if the conditional first two moments are misspecified. To alleviate these problems of possible misspecification, we consider weak GARCH representations characterized by an ARMA structure for the squared error terms. The weak GARCH representation eliminates the need for correct specification of the first two conditional moments. The parameters of the representation are estimated via two-stage least squares. The estimator is shown to be consistent and asymptotically normal. Forecasting issues are also addressed.