On Polynomial Cointegration in the State Space Framework
This paper deals with polynomial cointegration, i.e. with the phenomenon that linear combinations of a vector valued rational unit root process and lags of the process are of lower integration order than the process itself (for definitions see Section 2). The analysis is performed in the state space representation of rational unit root processes derived in Bauer and Wagner (2003). The state space framework is an equivalent alternative to the ARMA framework. Unit roots are allowed to occur at any point on the unit circle with arbitrary integer integration order. In the paper simple criteria for the existence of non-trivial polynomial cointegrating relationships are given. Trivial cointegrating relationships lead to the reduction of the integration order simply by appropriate differencing. The set of all polynomial cointegrating relationships is determined from simple orthogonality conditions derived directly from the state space representation. These results are important for analyzing the structure of unit root processes and their polynomial cointegrating relationships and also for the parameterization for system sets with given cointegration properties.
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- 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.
- 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.
- Hannes Leeb & Benedikt Poetscher, 1999. "The variance of an integrated process need not diverge to infinity," Econometrics 9907001, EconWPA.
- Johansen, S. & Schaumburg, E., 1997.
"Likelihood Analysis of Seasonal Cointegration,"
Economics Working Papers
eco97/16, European University Institute.
- Haldrup, Niels & Salmon, Mark, 1998. "Representations of I(2) cointegrated systems using the Smith-McMillan form," Journal of Econometrics, Elsevier, vol. 84(2), pages 303-325, June.
- Gregoir, Stephane & Laroque, Guy, 1994. "Polynomial cointegration estimation and test," Journal of Econometrics, Elsevier, vol. 63(1), pages 183-214, July.
- Dietmar Bauer & Martin Wagner, 2003.
"A Canonical Form for Unit Root Processes in the State Space Framework,"
dp0312, Universitaet Bern, Departement Volkswirtschaft.
- Dietmar Bauer & Martin Wagner, 2002. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0204, Universitaet Bern, Departement Volkswirtschaft.
- Gregoir, St phane, 1999.
"Multivariate Time Series With Various Hidden Unit Roots, Part Ii,"
Cambridge University Press, vol. 15(04), pages 469-518, August.
- Gregoir, St phane, 1999. "Multivariate Time Series With Various Hidden Unit Roots, Part I," Econometric Theory, Cambridge University Press, vol. 15(04), pages 435-468, August.
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