A Canonical Form for Unit Root Processes in the State Space Framework
In this paper we develop a canonical state space representation for rational stochastic processes containing unit roots with integer integration orders at arbitrary points on the unit circle. It is shown that the state space framework, which is -- in a certain sense made precise in the paper -- equivalent to the ARMA framework, is very suitable for the analysis of unit roots and cointegration issues. The advantages become especially prominent for systems with higher integration orders at the various roots on the unit circle. A unique state space representation is constructed that clearly reveals the integration and cointegration properties. The canonical form given in the paper can be used to construct a parameterization of the class of all rational processes with a given state space unit root structure, which is defined in the paper
|Date of creation:||Jul 2003|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: 0041 31 631 45 06
Fax: 41 31 631 37 83
Web page: http://www.vwi.unibe.ch/content/publikationen/index_eng.html
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dietmar Bauer & Martin Wagner, 2003. "On Polynomial Cointegration in the State Space Framework," Diskussionsschriften dp0313, Universitaet Bern, Departement Volkswirtschaft.
- Stock, James H & Watson, Mark W, 1993.
"A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems,"
Econometric Society, vol. 61(4), pages 783-820, July.
- James H. Stock & Mark W. Watson, 1991. "A simple estimator of cointegrating vectors in higher order integrated systems," Working Paper Series, Macroeconomic Issues 91-3, Federal Reserve Bank of Chicago.
- Tom Doan, . "SWDOLS: RATS procedure to estimate cointegrating vectors using dynamic OLS," Statistical Software Components RTS00207, Boston College Department of Economics.
- Johansen, Søren, 1992. "A Representation of Vector Autoregressive Processes Integrated of Order 2," Econometric Theory, Cambridge University Press, vol. 8(02), pages 188-202, June.
- Johansen, Soren & Schaumburg, Ernst, 1998.
"Likelihood analysis of seasonal cointegration,"
Journal of Econometrics,
Elsevier, vol. 88(2), pages 301-339, November.
- repec:cup:etheor:v:8:y:1992:i:2:p:188-202 is not listed on IDEAS
- Dietmar Bauer & Martin Wagner, 2000.
"Estimating Cointegrated Systems Using Subspace Algorithms,"
Econometric Society World Congress 2000 Contributed Papers
0293, Econometric Society.
- Bauer, Dietmar & Wagner, Martin, 2002. "Estimating cointegrated systems using subspace algorithms," Journal of Econometrics, Elsevier, vol. 111(1), pages 47-84, November.
- Dietmar Bauer & Martin Wagner, 2002. "Asymptotic Properties of Pseudo Maximum Likelihood Estimates for Multiple Frequency I(1) Processes," Diskussionsschriften dp0205, Universitaet Bern, Departement Volkswirtschaft.
- Gregoir, Stephane & Laroque, Guy, 1994. "Polynomial cointegration estimation and test," Journal of Econometrics, Elsevier, vol. 63(1), pages 183-214, July.
- Aoki, Masanao & Havenner, Arthur, 1989. "A method for approximate representation of vector-valued time series and its relation to two alternatives," Journal of Econometrics, Elsevier, vol. 42(2), pages 181-199, October.
- Gregoir, St phane, 1999.
"Multivariate Time Series With Various Hidden Unit Roots, Part I,"
Cambridge University Press, vol. 15(04), pages 435-468, August.
- Gregoir, St phane, 1999. "Multivariate Time Series With Various Hidden Unit Roots, Part Ii," Econometric Theory, Cambridge University Press, vol. 15(04), pages 469-518, August.
- Granger, C W J & Lee, T H, 1989. "Investigation of Production, Sales and Inventory Relationships Using Multicointegration and Non-symmetric Error Correction Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages S145-59, Supplemen.
- Banerjee, Anindya & Dolado, Juan J. & Galbraith, John W. & Hendry, David, 1993. "Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data," OUP Catalogue, Oxford University Press, number 9780198288107.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
- Hannes Leeb & Benedikt Poetscher, 1999. "The variance of an integrated process need not diverge to infinity," Econometrics 9907001, EconWPA.
When requesting a correction, please mention this item's handle: RePEc:ube:dpvwib:dp0312. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Silvia Glusstein-Gerber)
If references are entirely missing, you can add them using this form.