Cointegration in large VARs

The paper analyzes cointegration in vector autoregressive processes (VARs) for the cases when both number of coordinates, N, and time periods, T, are large same order. We propose a way to examine VAR order 1 presence based on modification Johansen likelihood ratio test. advantage our procedure over original test its finite sample corrections is that does not suffer from overrejection. This achieved through novel asymptotic theorems eigenvalues matrices statistic regime proportionally growing N T. Our theoretical findings supported by Monte Carlo simulations an empirical illustration. Moreover, we find surprising connection with multivariate analysis variance (MANOVA) explain why it emerges.