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A Canonical Form for Unit Root Processes in the State Space Framework

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Author Info
Dietmar Bauer
Martin Wagner

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Abstract

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

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Paper provided by Universitaet Bern, Departement Volkswirtschaft in its series Diskussionsschriften with number dp0312.

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Date of creation: Jul 2003
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Handle: RePEc:ube:dpvwib:dp0312

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Related research
Keywords: canonical form; state space representation; unit roots; cointegration;

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
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.:
  1. Johansen, Soren & Schaumburg, Ernst, 1998. "Likelihood analysis of seasonal cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 301-339, November. [Downloadable!] (restricted)
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  2. Dietmar Bauer & Martin Wagner, 2000. "Estimating Cointegrated Systems Using Subspace Algorithms," Econometric Society World Congress 2000 Contributed Papers 0293, Econometric Society. [Downloadable!]
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  3. Hannes Leeb & Benedikt Poetscher, 1999. "The variance of an integrated process need not diverge to infinity," Econometrics 9907001, EconWPA. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July. [Downloadable!] (restricted)
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  7. Dietmar Bauer & Martin Wagner, 2003. "On Polynomial Cointegration in the State Space Framework," Diskussionsschriften dp0313, Universitaet Bern, Departement Volkswirtschaft. [Downloadable!]
  8. Gregoir, Stephane & Laroque, Guy, 1994. "Polynomial cointegration estimation and test," Journal of Econometrics, Elsevier, vol. 63(1), pages 183-214, July. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. repec:cup:etheor:v:8:y:1992:i:2:p:188-202 is not listed on IDEAS
  11. Dietmar Bauer & Martin Wagner, 2002. "Asymptotic Properties of Pseudo Maximum Likelihood Estimates for Multiple Frequency I(1) Processes," Diskussionsschriften dp0205, Universitaet Bern, Departement Volkswirtschaft. [Downloadable!]
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Cited by:
(explanations, 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.)

  1. Dietmar Bauer & Martin Wagner, 2003. "On Polynomial Cointegration in the State Space Framework," Diskussionsschriften dp0313, Universitaet Bern, Departement Volkswirtschaft. [Downloadable!]
  2. Bauer, Dietmar & Wagner, Martin, 2005. "Autoregressive Approximations of Multiple Frequency I(1) Processes," Economics Series 174, Institute for Advanced Studies. [Downloadable!]
    Other versions:
  3. Helmut Luetkepohl, 2004. "Forecasting with VARMA Models," Economics Working Papers ECO2004/25, European University Institute. [Downloadable!]
    Other versions:
  4. Paruolo Paolo, 2005. "Design of vector autoregressive processes for invariant statistics," Economics and Quantitative Methods qf0504, Department of Economics, University of Insubria. [Downloadable!]
  5. Massimo Franchi, . "The Integration Order of Vector Autoregressive Processes," Discussion Papers 06-05, University of Copenhagen. Department of Economics. [Downloadable!]
    Other versions:
  6. Martin Wagner, 2002. "A Comparison of Johansen's, Bierens and the Subspace Algorithm Method for Cointegration Analysis," Diskussionsschriften dp0210, Universitaet Bern, Departement Volkswirtschaft. [Downloadable!]
    Other versions:
  7. Peter C.B. Phillips, 2004. "Automated Discovery in Econometrics," Cowles Foundation Discussion Papers 1469, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
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