Canonical Partial Autocorrelation Function of a Multivariate Time Series
多元时间序列的典型偏自相关函数
We propose a definition of the partial autocorrelation function $\beta(\cdot)$ for multivariate stationary time series suggested by the canonical analysis of the forward and backward innovations. Here $\beta(\cdot)$ satisfies $\beta(-n) = \beta(n)', n = 0, 1, \cdots,$ where $\beta(0)$ is nonnegative definite, $\{\beta(n), n = 1, 2, \cdots\}$ is a sequence of square matrices having singular values less than or equal to 1 and such that the order of $\beta(n + 1)$ is equal to…