英文文献：Testing Constancy of the Error Covariance Matrix in Vector Models against Parametric Alternatives using a Spectral Decomposition-使用谱分解测试向量模型中的误差协方差矩阵与参数替代的恒常性
英文文献作者：Yukai Yang
英文文献摘要：
I consider multivariate (vector) time series models in which the error covariance matrix may be time-varying. I derive a test of constancy of the error covariance matrix against the alternative that the covariance matrix changes over time. I design a new family of Lagrange-multiplier tests against the alternative hypothesis that the innovations are time-varying according to several parametric specifications. I investigate the size and power properties of these tests and find that the test with smooth transition specification has satisfactory size properties. The tests are informative and may suggest to consider multivariate volatility modelling.

我考虑了多变量(向量)时间序列模型，其中误差协方差矩阵可能是时变的。我推导了一个误差协方差矩阵的恒常性测试来对抗协方差矩阵随时间变化的备选项。针对创新是时变的假设，根据不同的参数规范，设计了一种新的拉格朗日乘子检验。对这些试验的尺寸和功率特性进行了研究，发现具有平滑过渡规格的试验具有令人满意的尺寸特性。测试内容丰富，可能建议考虑多元波动率建模。