A STATE SPACE CANONICAL FORM FOR UNIT ROOT PROCESSES
A STATE SPACE CANONICAL FORM FOR UNIT ROOT PROCESSES
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DOI：
10.1017/s026646661200014x
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发表时间：
2012-12-01
影响因子：
0.8
通讯作者：
Wagner, Martin
中科院分区：
文献类型：
--
作者：
Bauer, Dietmar;Wagner, Martin
本文给出了具有整数积分阶的单位根自回归滑动平均（阿尔马）过程在任意单位根频率下的正则状态空间表示。发达国家的代表利用一个特别简单的动态结构，这反过来又使得这种表示非常适合单位根，协整和多项式协整分析的状态过程。我们还提出了一个新的多项式协整定义，克服了现有定义的局限性，并扩展了格兰杰和李（1989 a，应用计量经济学杂志4，145-159）的I（2）过程的多元协整定义。统计分析的规范表示的一个主要目的是发展给定系统阶数的所有状态空间系统的集合的参数化，这些系统具有指定的单位根频率和积分阶数。这是，E。例如，在一个实施例中，用于伪最大似然估计。在这方面，与阿尔马表示相比，状态空间表示的优点在于，它容易允许对（协）积分性质进行限制。本文的结果举例说明的情况下，最感兴趣的应用工作。
In this paper we develop a canonical state space representation of autoregressive moving average (ARMA) processes with unit roots with integer integration orders at arbitrary unit root frequencies. The developed representation utilizes a state process with a particularly simple dynamic structure, which in turn renders this representation highly suitable for unit root, cointegration, and polynomial cointegration analysis. We also propose a new definition of polynomial cointegration that overcomes limitations of existing definitions and extends the definition of multicointegration for I(2) processes of Granger and Lee (1989a, Journal of Applied Econometrics 4, 145-159). A major purpose of the canonical representation for statistical analysis is the development of parameterizations of the sets of all state space systems of a given system order with specified unit root frequencies and integration orders. This is, e. g., useful for pseudo maximum likelihood estimation. In this respect an advantage of the state space representation, compared to ARMA representations, is that it easily allows one to put in place restrictions on the (co) integration properties. The results of the paper are exemplified for the cases of largest interest in applied work.