Tests for identification through heteroskedasticity in structural vector autoregressive analysis are developed for models with two volatility states where the time point of volatility change is known. The tests are Wald-type tests for which only the unrestricted model, including the covariance matrices of the two volatility states, has to be estimated. The residuals of the model are assumed to be from the class of elliptical distributions, which includes Gaussian models. The asymptotic null distributions of the test statistics are derived, and simulations are used to explore their small-sample properties. Two empirical examples illustrate the usefulness of the tests in applied work.

中文翻译：

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在结构矢量自回归模型中通过异方差测试识别

针对具有两个波动状态的模型开发了结构矢量自回归分析中的通过异方差鉴定的测试，其中波动率状态的时间点是已知的。检验是Wald型检验，仅需估计无限制模型（包括两个波动率状态的协方差矩阵）即可。假定模型的残差来自椭圆分布的类别，其中包括高斯模型。推导了测试统计量的渐近零分布，并使用模拟来探索其小样本属性。两个经验示例说明了测试在应用工作中的有用性。