EIASEVIER Economics Letters 51 (1996) 45-50 economics letters On cointegration tests for VAR models with drift Minxian Yang*, Ronald Bewley School of Economics, University of New South Wales, Sydney 2052, Australia Received 30 May 1995; accepted 10 October 1995 Abstract Following Bewley and Yang (Journal of the American Statistical Association, 1995, 90, 990-996), this paper considers cointegration tests that are based on the canonical correlation analysis(CCA) of Box and Tiao (Biometrika, 1977, 64, 355-365), for VAR models with drift. The critical values of the test statistics are shown to depend on the presence of drift. In addition, it is shown that the maximum eigenvalue from the CCA may b as an indicator for the presence of drift. Tables of critical values are also presented. Keywords: Error-correction models; Time trend; Asymptotic distributions JEL classification: C32 I. I n t rod uc ti on C o n s i d e r an n - d i m e n s i o n a l V A R ( k + 1) process, {y,}, g e n e r a t e d by k Ayt= -a/3'y,_ 1 + ~171jAyt_j + e, + ~ , (1) 1 w h e r e a, /3,//j and 6 are, respectively, n × r (0 < r <n), n × r, n × n and n × 1 matrices; {e,} is i.i.d, with a z e r o m e a n and a positive definite covariance matrix J2; and k is a constant integer. It is a s s u m e d that ( A 1 ) I ( I , - E ~ //jz/)(1 - z ) + a/3'z[ = 0 implies either ] z l > l or ? z = 1, and that (A2) the matrix • = a± (I n - E k 1 //j)/31 and ol±/31 are invertible, w h e r e a I and /3± are b o t h full ra nk n × (n - r) matrices satisfying a ' a ~ = 0 and/3'/31 = 0. T h e s e conditions e n s u r e that {y,} and {/3'y,} are, respectively, I(1) and I(0) and that y, can be written as y = y o + C ( ~ t + ~ e t ) + B ( L ) ( e - e o ) , (2) 1 * Corresponding author. Fax: +61-2-313-7691. 0165-1765/96/$12.00 © 1996 Elsevier Science S.A. All rights reserved SSDI 0165-1765(95)00783-0