Sequential Decision Rule
We are now ready to consider how to determine n - r, r2, and r1. In Chapter 3 i = 1, ..., n is the running index to denote the descending order of eigenvalues of the data covariance matrix. i is also associated with the principal component that corresponds to the i-th eigenvalue. Given n - r, r2, and r1, the principal components with i = 1, ..., n - r, with i = n - r + 1, ..., n - r + r2 ≡ n - r1, and with i = n - r1 + 1, ..., n each reveal asymptotically distinctive features. Thus i = 1, ..., n has been divided in three groups, Group ⊥ that consists of i = 1,..., n - r, Group 2 that consists of i = n - r + 1, ..., n - r + r2 ≡ n - r1, and Group 1 that consists of i = n - r1+1,...,n.
KeywordsUnit Root Limit Distribution Unit Root Test Grouping Method Trend Test
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