Autori: Salmon, Mark , Haldrup, Niels
Titolo: Polynomially cointegrated systems and their representations: a synthesis
Periodico: European University Institute of Badia Fiesolana (Fi). Department of Economics - Working papers
Anno: 1994 - Fascicolo: 8 - Pagina iniziale: 2 - Pagina finale: 29

This paper presents a discussion of polynomial cointegration and a synthesis of various ways generalised cointegrated systems for a multivariate time series process may be represented. Using the Smith-McMillan canonical form of a rational polynomial matrix we describe the null-space structure of higher order - and in particular 1(2) - cointegrated systems and we show how different representations such as the error correction model, the common stochastic trends model and various triangular array decompositions, can be derived within this unifying framework. Hence we extend the results of Hylleberg and Mizon (1989) to more general systems. The different representations provide different insights into distinct features of multivariate systems that may simultaneously contain several types of equilibrium behaviour. One obvious case arises when a model contains both higher order integrated and possibly seasonally integrated time series and can be represented in a lower dimensional space implying that the cointegrating equilibria may be expressed as polynomials in the lag operator. The implied long run equilibria may not then seem to be contemporanous in the underlying economic variables. Such non-contemporaneous equilibrium relationships may often have little appeal in terms of economic intuition and we briefly discuss how the specification of appropriately defined "state" variables may provide a more straightforward representation of economic equilibria for cointegrated systems


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Testo completo: http://hdl.handle.net/1814/488

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