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摘要翻译：
本文定义了具有有限型单位根的$\mathcal{H}$值自回归(AR)过程，其中$\mathcal{H}$是一个无限维可分Hilbert空间，并导出了Granger-Johansen表示定理的推广，该定理适用于任意积分阶$d=1,2,\dots$。一个存在性定理证明了有限型单位根AR的解必然是某个有限整数D的积分，并给出了具有有限个双边随机游动（累积）型公共趋势和无穷维协积分空间的公共趋势表示。一个刻划定理阐明了AR算子的结构与$(i)$积分阶，$(i)$吸引子空间和协整空间的结构，$(ii)$协整关系的表达式，$(iv)$过程的三角表示之间的联系。除0阶的协整关系数为无穷多外，$\mathcal{H}$值有限型单位根ARs的表示与一般有限维VAR的表示是一致的，对应于特例$\mathcal{H}=\mathbb{R}^p$。
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英文标题：
《Cointegration in functional autoregressive processes》
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作者：
Massimo Franchi and Paolo Paruolo
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最新提交年份：
2018
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分类信息：
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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英文摘要：
This paper defines the class of $\mathcal{H}$-valued autoregressive (AR) processes with a unit root of finite type, where $\mathcal{H}$ is an infinite dimensional separable Hilbert space, and derives a generalization of the Granger-Johansen Representation Theorem valid for any integration order $d=1,2,\dots$. An existence theorem shows that the solution of an AR with a unit root of finite type is necessarily integrated of some finite integer $d$ and displays a common trends representation with a finite number of common stochastic trends of the type of (cumulated) bilateral random walks and an infinite dimensional cointegrating space. A characterization theorem clarifies the connections between the structure of the AR operators and $(i)$ the order of integration, $(ii)$ the structure of the attractor space and the cointegrating space, $(iii)$ the expression of the cointegrating relations, and $(iv)$ the Triangular representation of the process. Except for the fact that the number of cointegrating relations that are integrated of order 0 is infinite, the representation of $\mathcal{H}$-valued ARs with a unit root of finite type coincides with that of usual finite dimensional VARs, which corresponds to the special case $\mathcal{H}=\mathbb{R}^p$.
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PDF链接：
https://arxiv.org/pdf/1712.07522
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