Testing the Rank of a Sub-Matrix of Cointegration with a Deterministic Trend

In this paper we consider the test of the rank of the sub-matrix of b, the cointegrating matrix, when the process has a deterministic linear trend. We review the problem of the testing procedure proposed by Kurozumi (2003) and give the alternative test statistic that is symptotically chi-square distributed. We also propose the test of the rank of the sub-matrix of d, the orthogonal matrix to b. Monte Carlo simulations show that our tests proposed in this paper work fairly well in finite samples even when the tests proposed by Kurozumi (2003) perform poorly.