The Multivariate Portmanteau Statistic
将Box和Pierce提出的单变量ARMA模型混合检验扩展到多元ARMA模型，检验统计量可表示为拟合模型残差协方差的函数，并推导了适用于小样本的修正形式，通过模拟比较了两种统计量的性质。
Box and Pierce have derived a goodness-of-fit test, the portmanteau test, for univariate autoregressive moving-average (ARMA) time series models. This test is here extended to multivariate ARMA models; the test statistic may be conveniently expressed as a function of the covariances between the residuals of the fitted model. A modified form of the statistic designed to have superior properties in small samples is derived, and the two forms of the statistic are compared via computer simulation.