EES 0836 Study Guide - Quiz Guide: Asteroid Family, Cointegration
27 May 2016
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This gives the solutions = 6 and = 3. The characteristic roots are also known as eigenvalues. The rank of a matrix is equal to the number of linearly independent rows or columns in the matrix. The rank of a matrix is equal to the order of the largest square matrix we can obtain from. For example, the determinant of above 0, therefore it has rank 2. Some properties of the eigenvalues of any square matrix a: 1. the sum of the eigenvalues is the trace. 2. the product of the eigenvalues is the determinant. 3. the number of non-zero eigenvalues is the rank. Returning to johansen"s test, the vecm representation of the var was (cid:1)yt = yt-1 + 1 yt-1 + 2 yt-2 + + k-1 yt-(k-1) + ut. The test for cointegration between the y"s is calculated by looking at the rank of the matrix via its eigenvalues. (to prove this requires some technical intermediate steps).
