On Polynomial Cointegration in the State Space Framework

Dietmar Bauer and Martin Wagner

Diskussionsschriften from Universitaet Bern, Departement Volkswirtschaft

Abstract: 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.

Keywords: Unit roots; polynomial cointegration; state space representation (search for similar items in EconPapers)
JEL-codes: C13 C32 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2003-07
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Persistent link: http://EconPapers.repec.org/RePEc:ube:dpvwib:dp0313

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