块循环矩阵与多元平稳序列的谱

IF 0.8 Q2 MATHEMATICS
M. Bolla, T. Szabados, Máté Baranyi, Fatma Abdelkhalek
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引用次数: 0

摘要

摘要给定一个具有绝对可和自协方差的弱平稳多变量时间序列,证明了前n个自协方差的块Toeplitz矩阵的特征值与谱密度矩阵在n个傅立叶频率上的谱并集之间的渐近关系→ ∞. 对于证明,使用了块循环矩阵的特征值和特征向量。已证明的定理对于时域和频域计算之间的类比具有重要的意义。特别地,复数主分量被用于过程的低秩近似;而块Toeplitz矩阵的块Cholesky分解引起了创新子空间内的降维。结果在一个金融时间序列上进行了说明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Block circulant matrices and the spectra of multivariate stationary sequences
Abstract Given a weakly stationary, multivariate time series with absolutely summable autocovariances, asymptotic relation is proved between the eigenvalues of the block Toeplitz matrix of the first n autocovariances and the union of spectra of the spectral density matrices at the n Fourier frequencies, as n → ∞. For the proof, eigenvalues and eigenvectors of block circulant matrices are used. The proved theorem has important consequences as for the analogies between the time and frequency domain calculations. In particular, the complex principal components are used for low-rank approximation of the process; whereas, the block Cholesky decomposition of the block Toeplitz matrix gives rise to dimension reduction within the innovation subspaces. The results are illustrated on a financial time series.
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来源期刊
Special Matrices
Special Matrices MATHEMATICS-
CiteScore
1.10
自引率
20.00%
发文量
14
审稿时长
8 weeks
期刊介绍: Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.
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