Summary
This paper discussed the role of the drift in vector autoregressive processes allowing for integrated components up to order 2. It is shown how the drift can generate linear and quadratic deterministic trends. A two-stage statistical analysis of the system in the presence of quadratic trends is proposed. The analysis of the system allows to define a consistent sequence of tests on the numbers of common components integrated of a given order, called the integration indices of the system. The relevant asymptotic distributions are non-standard, belong to the Limiting Gaussian Functional family and are tabulated by simulation. The proposed procedure can also be consistently combined with other procedures proposed by the author for the cases of a linear trend and of no deterministic trends in the system.
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Invited paper at the Conference held in Bologna, Italy, 27–28 May 1993, on “Statistical Tests: Methodology and Econometric Applications”.
Partial financial support is acknowledged from Italian MURST grants 40% and 60%.
An erratum to this article is available at http://dx.doi.org/10.1007/BF03178904.
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Paruolo, P. The role of the drift in I(2) systems. J. It. Statist. Soc. 3, 93–123 (1994). https://doi.org/10.1007/BF02589043
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DOI: https://doi.org/10.1007/BF02589043