Testing for the cointegrating rank of a vector autoregressive process with uncertain deterministic trend term

Abstract

Summary When applying Johansen's procedure for determining the cointegrating rank to systems of variables with linear deterministic trends, there are two possible tests to choose from. One test allows for a trend in the cointegration relations and the other one restricts the trend to being orthogonal to the cointegration relations. The first test is known to have reduced power relative to the second one if there is in fact no trend in the cointegration relations, whereas the second one is based on a misspecified model if the linear trend is not orthogonal to the cointegration relations. Hence, the treatment of the linear trend term is crucial for the outcome of the rank determination procedure. We compare three alternative procedures, which are applicable if there is uncertainty regarding the proper trend specification. In the first one a specific cointegrating rank is rejected if one of the two tests rejects, in the second one the trend term is decided upon by a pretest and in the third procedure only tests which allow for an unrestricted trend term are used. We provide theoretical asymptotic and small sample simulation results, which show that the first strategy is preferable in applied work.

Comparison of procedures for fitting the autoregressive order of a vector error correction model

“…This kind of DGP is used in numerous studies (e.g. Hubrich et al (2001) or Demetrescu et al (2009)). In addition the results concerning the information criteria are corroborated by previous studies.…”

Robust cointegration testing in the presence of weak trends, with an application to the human origin of global warming

“…There has been a recent renewed interest in designing testing strategies for unit roots that are robust to the possible presence or a linear trend, see Harvey, Leybourne and Taylor (2008) and the multivariate extension in Demetrescu, Lütkepohl and Saikkonen (2009). These studies draw on the long established difficulties in distinguishing in finite samples between stochastic and deterministic trends, see e.g.…”

“…In view of the difficulties associated with disentangling stochastic and deterministic trends, Demetrescu, Lütkepohl and Saikkonen (2009) have proposed extending the work by Harvey, Leybourne and Taylor (2008) to the vector autoregressive (VAR) process. The technique they recommend consists in estimating two models with a deterministic trend that is either-or not-restricted to lie in the space orthogonal to the cointegrating vector; the test rejects the null if one of the statistics is significant.…”

“…The question we address here concerns the behavior of the combination method when the trend is hardly noticeable so its absence cannot be rejected at conventional significance levels. We assess whether the approach recommended by Demetrescu et al (2009) still holds then. This situation may occur when the power of the t-test for the null of no linear trend is low, say less than 50%.…”

“…Why do we assess the recommendation of Demetrescu et al (2009) in the presence of local trends? The rationale behind their choice of test statistics is that they combine (i) one which is robust to trends but inefficient in their absence and (ii) another which is inconsistent in the presence of trends.…”