ELSEVIER Economics Letters 49 (1995) 137-145 economics letters A note on the critical values for the maximum likelihood (seasonal) cointegration tests" Hahn S. Lee a, Pierre L. Siklos b'* "Department of Economics, Tulane University, 206 Tilton Hall, New Orleans, LA 70118, USA bDepartment of Economics, Wilfrid Laurier University, Waterloo, Ont., N2L 3C5, Canada Received 21 March 1994; revised version received 3 January 1995; accepted 2(I January 1995 Abstract In this paper the finite sample distributions of the Johansen procedure for cointegration tests using seasonally unadjusted data are presented and compared with the asymptotic distributions. In particular, we consider the data generating process which contains unit roots at the seasonal and zero frequencies, as well as a trend. Keywords: Seasonal cointegration; Maximum likelihood inference; Finite sample distribution; Asymptotic distribution JEL classification: C32 1. Introduction Following the seminal work by Engle and Granger (1987), there has been a great deal of interest in cointegrating relationships among economic time series. Among various estimation and testing procedures for cointegration, the maximum likelihood (ML) approach based on Gaussian VAR models developed in Johansen (1988, 1991) has received particular attention. Since tests for cointegration involve statistics with non-standard asymptotic distributions which are expressed as functionals of Brownian motions, the critical values for the cointegration tests ~'~ The first author acknowledges the support of the Bureau of the Census where part of the research was completed while he was a participant in the ASA/NSF/Census Research Program. The second author acknowl- edges the financial support of Wilfrid Laurier University through a short-term research grant and the hospitality of University of California at San Diego where this research was partly carried out while he was visiting UCSD. Helpful comments by an anonymous referee are also greatly appreciated. * Corresponding author. Elsevier Science B.V. SSDI 0165-1765(95)00655-9