Banach空间上自回归时间序列的自然分量
The natural components of an autoregressive time series on Banach space
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中文总结 AI 辅助
本文证明Banach空间上的自回归时间序列可典范分解为有限个自包含自然分量的直积，各分量由特征线性束谱点对应的谱投影定义，并依据谱点位置确定边界条件。
中文摘要 AI 辅助
我们证明，Banach空间上的自回归时间序列可以通过特征线性束的每个谱点的谱投影，典范地等同于定义在分离子空间上的有限个自包含且自决定的自然分量的直积。我们假设该束的预解式除谱点外处处解析，谱点可以是极点或孤立本性奇点。每个自然分量表示为前向、后向或外向流，由遥远的过去、遥远的未来或指定的初始时间处的上游边界条件固定——具体取决于相应的谱点位于单位圆外、单位圆内或单位圆上。
英文摘要
We show that an autoregressive time series on Banach space can be canonically identified with a finite direct product of self-contained and self-determined natural components defined on separate subspaces by the spectral projections for each spectral point of the characteristic linear pencil. We assume the resolvent of the pencil is analytic everywhere except for the spectral points which may be poles or isolated essential singularities. Each natural component is represented as a forward, backward or outward flow fixed by an upstream boundary condition in the far distant past, the far distant future, or at a nominated initial time---depending on whether the corresponding spectral point is outside, inside, or on the unit circle.
发表机构
- University of South Australia（南澳大学）
- University of Sydney（悉尼大学）
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