A STATE SPACE CANONICAL FORM FOR UNIT ROOT PROCESSES

Dietmar Bauer () and Martin Wagner

Econometric Theory, 2012, vol. 28, issue 6, 1313-1349

Abstract: 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 Econometrics4, 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.

Date: 2012
References: Add references at CitEc
Citations: View citations in EconPapers (15)

Downloads: (external link)
https://www.cambridge.org/core/product/identifier/ ... type/journal_article link to article abstract page (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cup:etheor:v:28:y:2012:i:06:p:1313-1349_00

Access Statistics for this article

More articles in Econometric Theory from Cambridge University Press Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK.
Bibliographic data for series maintained by Kirk Stebbing ().