Tests of the co-integration rank in VAR models in the presence of a possible break in trend at an unknown point

Harris, David; Leybourne, Stephen J.; Taylor, A.M. Robert

Abstract

In this paper we consider the problem of testing for the co-integration rank of a vector autoregressive process in the case where a trend break may potentially be present in the data. It is known that un-modelled trend breaks can result in tests which are incorrectly sized under the null hypothesis and inconsistent under the alternative hypothesis. Extant procedures in this literature have attempted to solve this inference problem but require the practitioner to either assume that the trend break date is known or to assume that any trend break cannot occur under the co-integration rank null hypothesis being tested. These procedures also assume the autoregressive lag length is known to the practitioner. All of these assumptions would seem unreasonable in practice. Moreover in each of these strands of the literature there is also a presumption in calculating the tests that a trend break is known to have happened. This can lead to a substantial loss in finite sample power in the case where a trend break does not in fact occur. Using information criteria based methods to select both the autoregressive lag order and to choose between the trend break and no trend break models, using a consistent estimate of the break fraction in the context of the former, we develop a number of procedures which deliver asymptotically correctly sized and consistent tests of the co-integration rank regardless of whether a trend break is present in the data or not. By selecting the no break model when no trend break is present, these procedures also avoid the potentially large power losses associated with the extant procedures in such cases.

Citation

Harris, D., Leybourne, S. J., & Taylor, A. R. (2016). Tests of the co-integration rank in VAR models in the presence of a possible break in trend at an unknown point. Journal of Econometrics, 192(2), 451-467. https://doi.org/10.1016/j.jeconom.2016.02.010

• Journal Article Type: Article
• Acceptance Date: Jan 2, 2016
• Online Publication Date: Feb 11, 2016
• Publication Date: 2016-06
• Deposit Date: Feb 17, 2016
• Publicly Available Date: Feb 17, 2016
• Journal: Journal of Econometrics
• Print ISSN: 0304-4076
• Electronic ISSN: 1872-6895
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 192
• Issue: 2
• Pages: 451-467
• DOI: https://doi.org/10.1016/j.jeconom.2016.02.010
• Keywords: Co-integration rank; vector autoregression; error-correction model; trend break; break point estimation; information criteria
• Public URL: https://nottingham-repository.worktribe.com/output/796773
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0304407616300136
• Contract Date: Feb 17, 2016