Tests of the cointegration rank in VAR models in the presence of a possible break in trend at an unknown pointTools Harris, David, Leybourne, Stephen J. and Taylor, A.M. Robert (2016) Tests of the cointegration rank in VAR models in the presence of a possible break in trend at an unknown point. Journal of Econometrics, 192 (24). pp. 451467. ISSN 03044076
AbstractIn this paper we consider the problem of testing for the cointegration rank of a vector autoregressive process in the case where a trend break may potentially be present in the data. It is known that unmodelled 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 cointegration 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 cointegration 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.
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