Generalized Rouche's theorem and its application to multivariate autoregressions
Generalized Rouche's theorem and its application to multivariate autoregressions
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广义 Rouche 定理及其在多元自回归中的应用
DOI：
10.1109/tassp.1980.1163469
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发表时间：
1980
期刊：
影响因子：
--
通讯作者：
S. Arimoto
中科院分区：
文献类型：
--
作者：
Y. Monden;S. Arimoto
本文将Rouche定理推广到多项式矩阵零点的位置。然后将该定理应用于Levinson-Wiggins-罗宾逊（LWR）算法，以便在递归的每一步枚举多项式矩阵的零点，并测试拟合的多元自回归的稳定性。在LWR算法中，广泛地利用了一些重要的代数关系，这些关系是由可对称化矩阵的性质导出的。本文假定只给出有限时间间隔内由观测数据计算的样本相关矩阵的有限序列，因此由其傅里叶变换定义的谱密度矩阵不一定非负定。
This paper proposes the matrix extension of Rouche's theorem to investigate the location of zeros of polynomial matrices. The theorem is then applied to the Levinson-Wiggins-Robinson (LWR) algorithm in order to enumerate the zeros of a polynomial matrix at each step of the recursion and test the stability of fitted multivariate autoregressions. Extensive use is made of some important algebraic relations in the LWR algorithm, which are derived from the properties of symmetrizable matrices. In this paper, only a finite sequence of sample correlation matrices computed from obsereed data over a finite time interval is assumed to be given and, therefore, the spectral density matrix defined by its Fourier transform is not necessarily nonnegative definite.