The manuscript studies testing methods in systems with relationships between observed variables and conditional variances drawn from popular multivariate GARCH models. Although these methods have been extensively used to study the effects of uncertainty proxied by GARCH variables, inferential results are absent under misspecification or when using multi-step estimators. Concentrating on test statistics for the hypothesis of no uncertainty impact, extensive Monte Carlo evidence is presented. Results show that severe size distortion and low power can occur when using two-step procedures unless existing heteroskedasticity is modelled at every stage. In contrast, under moderate unconditional residual cross-correlation, joint estimation of all model parameters yields test statistics with impressive relative power. In terms of misspecification, the consequences of ignoring asymmetries in the conditional variance matrix are shown to be potentially severe. Otherwise, estimation of DCC and diagonal BEKK models may be preferred relative to extended DCC and full BEKK counterparts, even under weak negative volatility spillovers. Issues are highlighted with an analysis of the relationships between production growth, inflation and their volatilities.

中文翻译：

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错误指定的 GARCH-M 模型中的推理*

该手稿研究了系统中的测试方法，这些方法具有观察变量和从流行的多元 GARCH 模型中提取的条件方差之间的关系。尽管这些方法已被广泛用于研究 GARCH 变量所代表的不确定性的影响，但在错误指定或使用多步估计量时没有推论结果。集中于无不确定性影响假设的检验统计，提供了广泛的蒙特卡罗证据。结果表明，除非在每个阶段都对现有的异方差性进行建模，否则使用两步程序时可能会出现严重的尺寸失真和低功率。相比之下，在适度的无条件残差互相关下，所有模型参数的联合估计会产生具有令人印象深刻的相对功效的测试统计数据。在规格错误方面，忽略条件方差矩阵中的不对称性的后果显示出可能很严重。否则，相对于扩展的 DCC 和完整的 BEKK 模型，DCC 和对角 BEKK 模型的估计可能更受欢迎，即使在微弱的负波动溢出情况下也是如此。通过分析生产增长、通货膨胀及其波动之间的关系，突出了这些问题。