Error Bands for Impulse Responses
展示了如何将简化型VAR的误差带方法正确扩展到过度识别模型，并建议用基于似然的形状不确定性带补充传统逐点带，避免经典置信区间的误导。
We show how correctly to extend known methods for generating error bands in reduced form VAR's to overidentified models. We argue that the conventional pointwise bands common in the literature should be supplemented with measures of shape uncertainty, and we show how to generate such measures. We focus on bands that characterize the shape of the likelihood. Such bands are not classical confidence regions. We explain that classical confidence regions mix information about parameter location with information about model fit, and hence can be misleading as summaries of the implications of the data for the location of parameters. Because classical confidence regions also present conceptual and computational problems in multivariate time series models, we suggest that likelihood-based bands, rather than approximate confidence bands based on asymptotic theory, be standard in reporting results for this type of model.