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THE INTEGRATION ORDER OF VECTOR AUTOREGRESSIVE PROCESSES

Published online by Cambridge University Press:  05 April 2007

Massimo Franchi
Massimo Franchi
Affiliation:
Università di Roma “La Sapienza”
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Abstract

We show that the order of integration of a vector autoregressive process is equal to the difference between the multiplicity of the unit root in the characteristic equation and the multiplicity of the unit root in the adjoint matrix polynomial. The equivalence with the standard I(1) and I(2) conditions (Johansen, 1996, Likelihood-Based Inference in Cointegrated Vector Auto-Regressive Models) is proved.I am very grateful to Søren Johansen for his precious insights and his continuous help throughout the development of the paper. I also thank Paolo Paruolo (the coeditor) and the referees for valuable feedback. This paper was written while the author was a Post Doc at the Department of Economics, University of Copenhagen, and the hospitality of this institution is gratefully acknowledged.

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 23 , Issue 3 , June 2007 , pp. 546 - 553
Copyright
© 2007 Cambridge University Press

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References

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