Testing for the Cointegrating Rank of a Var Process With An Intercept

Abstract

Testing the cointegrating rank of a vector autoregressive process with an intercept is considered. In addition to the likelihood ratio (LR) tests developed by Johansen and Juselius and others we also consider an alternative class of tests which is based on estimating the trend parameters of the deterministic term in a di erent w ay. The asymptotic local power of these tests is derived and compared to that of the corresponding LR tests. The small sample properties are investigated by simulations. The new tests are seen to be substantially more powerful than conventional LR tests.We are grateful to the Deutsche Forschungsgemeinschaft, SFB 373, for nancial support and to Christian M uller and Kirstin Hubrich for performing the computations.

Determining p-values for systems cointegration tests with a prior adjustment for deterministic terms

“…Following Doornik (1998) and Johansen et al (2000) I have presented a procedure to approximate the asymptotic distributions of systems cointegration tests with a prior adjustment for deterministic terms suggested by Lütkepohl et al (2004), Saikkonen & Lütkepohl (2000a, 2000b, 2000c and Saikkonen & Luukkonen (1997). These tests make different assumptions on the inclusion of deterministic components like a mean term, a linear trend or a level shift.…”

“…The test version of Saikkonen & Lütkepohl (2000a) is similar to the one in Saikkonen & Lütkepohl (2000c) with a linear trend but considers the restriction that the linear trend is orthogonal to the cointegration space. Therefore, the restriction τ = β µ 1 = 0 is imposed within the RR regression and secondly, the adjustment of the data occurs according to the …”

“…The reason is that the cointegrating ranks specified both under the null and the alternative hypothesis have to be smaller than the system dimension due to the orthogonal trend (see Saikkonen & Lütkepohl 2000a). Accordingly, we obtain 140 simulation sets for these two distributions.…”

“…In this paper I present a procedure to approximate the asymptotic distributions of systems cointegration tests with a prior adjustment for deterministic terms suggested by Lütkepohl et al (2004), Saikkonen & Lütkepohl (2000a, 2000b, 2000c and Saikkonen & Luukkonen (1997). The asymptotic distributions are approximated by the Gamma distribution and the parameters necessary to fit the Gamma distributions are obtained from response surfaces which I describe in this paper.…”

“…A similar test with a mean term only is due to Saikkonen & Luukkonen (1997). Finally, Saikkonen & Lütkepohl (2000a) consider a linear trend that is orthogonal to the cointegration space. Furthermore, seasonal dummy variables can be incorporated into all procedures without changing the asymptotic results.…”