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Multivariate Time Series: A Polynomial Error Correction Representation Theorem

Published online by Cambridge University Press:  11 February 2009

Stéphane Gregoir  and
Guy Laroque
Stéphane Gregoir
Affiliation:
Institut National de la Statistique et des Etudes Economiques
Guy Laroque
Affiliation:
Institut National de la Statistique et des Etudes Economiques
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Abstract

We consider a class of multivariate processes which, when differenced enough, yield covariance stationary processes whose determinants of the Wold representation have I as their only root on the unit circle. A representation theorem is proved for this class of processes that generalizes the Granger representation theorem.

Type
Articles
Information
Econometric Theory , Volume 9 , Issue 3 , June 1993 , pp. 329 - 342
Copyright
Copyright © Cambridge University Press 1993

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References

1.Cartan, H.Théorie Élémentaire des Fonctions Analytiques. Paris: Hermann, 1961.Google Scholar
2.Dieudonné, J.Eléments d'Analyse I: Fondements de l'Analyse Moderne. Paris: Gauthier-Villars, 1969.Google Scholar
3.Engle, R.F. & Granger, C.W.J.. Co-integration and error correction: Representation, estimation and testing. Econometrica 55 (1987): 251–276.CrossRefGoogle Scholar
Engle, R.F. & Yoo, B.S.. Cointegrated economic time series: A survey with new results. In Engle, R.F. & Granger, C.W.J. (eds.), Long-Run Economic Relationships: Readings in Cointegration. Oxford: Oxford University Press, 1991.CrossRefGoogle Scholar
5.Granger, C.W.J.Some properties of time series data and their use in econometric model specification. Journal of Econometrics (1981): 121–130.CrossRefGoogle Scholar
6.Granger, C.W.J. & Lee, T.H.. Investigation of production, sales and inventory relationships using multicointegration and non-symmetric error correction models. Journal of Applied Econometrics 4 (1989): 145–159.CrossRefGoogle Scholar
Granger, C.W.J. & Lee, T.H.. Multicointegration. In Rhodes, G.F. Jr. & Fomby, T.B. (eds.), Advances in Econometrics: Cointegration, Spurious Regressions and Unit Roots. Greenwich, CT: JAI Press, 1989.Google Scholar
Granger, C.W.J. & Weiss, A.A.. Time series analysis of error correcting models. In Karlin, S., Amemiya, T., & Goodman, L.A. (eds.), Studies in Economic Time Series and Multivariate Statistics. New York: Academic Press, 1983.Google Scholar
Hendry, D.F. & Ungern-Sternberg, T. Von. Liquidity and inflation effects on consumer's expenditure. In Deaton, A.S. (ed.), Essays in the Theory and Measurement of Consumer's Behavior. Cambridge: Cambridge University Press, 1981.Google Scholar
10.Johansen, S.The mathematical structure of error correction models. Contemporary Mathematics 80 (1988): 359–386.CrossRefGoogle Scholar
11.Johansen, S.A representation of vector autoregressive processes integrated of order 2. Econometric Theory (to appear).Google Scholar
12.Phillips, P.C.B. & Solo, V.. Asymptotics for linear processes. Annals of Statistics 20 (1992): 971–1001.CrossRefGoogle Scholar
13.Sims, C.A.Money, income and causality. American Economic Review 62 (1972): 540–552.Google Scholar
14.Sims, C.A.Macroeconomics and reality. Econometrica 48 (1980): 1–48.CrossRefGoogle Scholar