Unit Root Tests
We shall prove that the minor, nonstandard terms in principal components do not affect the applicability of the unit root tests. Both the univariate and the multivariate unit root tests are considered. The univariate unit root test, which is the well known method in Perron (1989), is expected to be applied to each individual principal component in Group ⊥, one principal component in Group 2 when r2 = 1, and each individual component in Group 1. The test will be described in Section 5.1. It will be followed in Sections 5.2 and 5.3 by our proofs of its applicability to the principal components in Group ⊥, and in Section 5.4 by its applicability to Group 2 and Group 1. The multivariate unit root test is a test for zero cointegration rank in Johansen et al. (2000). It is expected to be applied to the entire set of principal components in Group 2 when r2 ≥ 2. The method will be described in Section 5.5, and our proof of its applicability to Group 2 will be given in Section 5.6. So far we have assumed that the correct division among Groups ⊥, 2, and 1 is known, and that the division is used to assign the correct unit root tests to the principal components. In Section 5.7, we shall analyse the effects that incorrect divisions among the three Groups would bring about.
KeywordsUnit Root Test Cointegration Vector Stationary ARMA Cointegration Rank Standard Time Series
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