The asymptotic distribution of canonical correlations and variates in cointegrated models

The cointegrated model considered here is a nonstationary vector autoregressive process in which some linear functions are stationary and others are random walks. The first difference of the process (the “error-correction form“) is stationary. Statistical inference, such as reduced rank regression estimation of the coefficients of the process and tests of hypotheses of dimensionality of the stationary part, involves the canonical correlations between the difference vector and the relevant vector of the past of the process. The asymptotic distributions of the canonical correlations and the canonical vectors under the assumption that the process is Gaussian are found.