ESTIMATION OF MULTIVARIATE TIME SERIES
ESTIMATION OF MULTIVARIATE TIME SERIES
复制标题
多元时间序列的估计
DOI：
10.1111/j.1467-9892.1987.tb00423.x
复制
发表时间：
1987
影响因子：
0.9
通讯作者：
B. L. Shea
中科院分区：
文献类型：
--
作者：
B. L. Shea
。本文提出的算法是Pearlman（1980）讨论的计算单变量ARMA模型精确似然的过程的多元推广。Ansley和Kohn（1983）已经展示了当并非所有观测值都已知时，如何使用卡尔曼滤波器来计算精确的似然函数。在Shea（1983）中表明，除了ARMA（2,1）和一对低阶AR过程之外，对于所有ARMA模型，该算法比Ansley和Kohn（1983）的算法快得多，因此当我们没有缺失观测时，应该使用该算法。NAG（1987）库中的Fortran子程序G13DCF使用该算法的改编来拟合矢量ARMA模型。使用此例程的经验表明，对ARMA参数矩阵，特别是残差协方差矩阵进行合理的初始估计，不仅可以大大减少计算时间，而且更重要的是提高了最小化过程的收敛性。因此，我们提出了一种计算ARMA参数初始估计的方法，该方法涉及使用从单变量到多变量情况的逆交叉协方差概念的推广。最后，将理论应用于实际时间序列的二元模型拟合。
. The algorithm proposed here is a multivariate generalization of a procedure discussed by Pearlman (1980) for calculating the exact likelihood of a univariate ARMA model. Ansley and Kohn (1983) have shown how the Kalman filter can be used to calculate the exact likelihood function when not all the observations are known. In Shea (1983) it is shown that this algorithm is much quicker than that of Ansley and Kohn (1983) for all ARMA models except an ARMA (2, 1) and a couple of low-order AR processes and therefore when we have no missing observations this algorithm should be used instead. The Fortran subroutine G13DCF in the NAG (1987) Library fits a vector ARMA model using an adaptation of this algorithm. Experience in the use of this routine suggests that having reasonably good initial estimates of the ARMA parameter matrices, and in particular the residual error covariance matrix, can not only substantially reduce the computing time but more important improve the convergence properties of the minimization procedure. We therefore propose a method of calculating initial estimates of the ARMA parameters which involves using a generalization of the concept of inverse cross covariances from the univariate to the multivariate case. Finally theory is put into practice with the fitting of a bivariate model to a couple of real-life time series.