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The Cointegrated VAR without Unit Roots Representation Theory and Asymptotics

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Document pages: 39 pages

Abstract: It has been known since Elliott (1998) that efficient methods of inference oncointegrating relationships break down when autoregressive roots are near butnot exactly equal to unity. This paper addresses this problem within theframework of a VAR with non-unit roots. We develop a characterisation ofcointegration, based on the impulse response function implied by the VAR, thatremains meaningful even when roots are not exactly unity. Under thischaracterisation, the long-run equilibrium relationships between the series areidentified with a subspace associated to the largest characteristic roots ofthe VAR. We analyse the asymptotics of maximum likelihood estimators of thissubspace, thereby generalising Johansen s (1995) treatment of the cointegratedVAR with exactly unit roots. Inference is complicated by nuisance parameterproblems similar to those encountered in the context of predictive regressions,and can be dealt with by approaches familiar from that setting.

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