Estimation and hypothesis testing of cointegration

Estimating cointegrating relationships requires specific techniques. Canonical correlations are used to determine the rank and space of the cointegrating matrix. The vectors used to transform the data into canonical variables have an eigenvector representation, and the associated canonical correlations have an eigenvalue representation. The number of cointegrating relations is chosen based upon a theoretical difference in the convergence rates of the eignevalues. The number of cointegrating relations is consistently estimated using a threshold function which places a lower bound on the eigenvalues associated with cointegrating relations and an upper bound on the eigenvalues on the eigenvalues not associated with cointegrating relations. The proposed estimator performs better with a large number of cross-sectional observations and moderate time series length.