Testing for cointegration at any frequency using spectral methods

Summary In this paper a new simple test for cointegration at any frequency is presented. This method can thus be applied to test for cointegration both at the zero and at the seasonal frequencies. It requires the estimation of the coherency spectrum of weakly stationary processes, therefore only standard spectral theory is involved. The testing procedure is similar to the one suggested by Phillips and Ouliaris (1988) and recently generalized by Joyeux (1992) to frequencies different from zero, but it does not suffer of some problems connected with the use of principal components methods in the frequency domain. Invited paper at the Conference held in Bologna, Italy, 27–28 May 1993, on ?Statistical Tests: Methodology and Econometric Applications?.