This paper provides a residual-based approach to examine the adequacy of multivariate GARCH models. We employ the transformed quadratic residuals to construct the residual-based statistic and derive its correct asymptotic distribution by taking into account the impact of parameter estimation uncertainty. The simulation results indicate that the residual-based test achieves reasonable sizes and comparable powers. An empirical application further shows the usefulness of the proposed test.

中文翻译：

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使用变换二次残差对多元 GARCH 模型进行基于残差的检验

本文提供了一种基于残差的方法来检查多变量 GARCH 模型的充分性。我们采用转换后的二次残差来构建基于残差的统计量，并通过考虑参数估计不确定性的影响推导出其正确的渐近分布。仿真结果表明，基于残差的测试达到了合理的大小和可比的功效。实证应用进一步表明了所提出的测试的有用性。