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摘要翻译：
我们推广了I(1)和I(2)向量自回归过程的Granger-Johansen表示定理，以适应取值于任意复可分Hilbert空间的过程。这种更一般的设置对于涉及功能时间序列的统计应用具有中心意义。首先得到了全纯指数零Fredholm算子铅笔的逆极点为一阶或二阶的充要条件。这些条件构成了我们发展自回归Hilbertian过程的I(1)和I(2)表示的基础。利用自回归算子pencil在一个邻域内的行为刻画了协整子空间和吸引子空间。
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英文标题：
《Representation of I(1) and I(2) autoregressive Hilbertian processes》
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作者：
Brendan K. Beare and Won-Ki Seo
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最新提交年份：
2019
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We extend the Granger-Johansen representation theorems for I(1) and I(2) vector autoregressive processes to accommodate processes that take values in an arbitrary complex separable Hilbert space. This more general setting is of central relevance for statistical applications involving functional time series. We first obtain a range of necessary and sufficient conditions for a pole in the inverse of a holomorphic index-zero Fredholm operator pencil to be of first or second order. Those conditions form the basis for our development of I(1) and I(2) representations of autoregressive Hilbertian processes. Cointegrating and attractor subspaces are characterized in terms of the behavior of the autoregressive operator pencil in a neighborhood of one.
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PDF链接：
https://arxiv.org/pdf/1701.08149
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