ABSTRACT
Hylleberg et al. ( 1990) pointed out that in case of several spectral poles, as for example x1 in Eq. (3.8) the procedure in Engle and Granger (1987) to test for cointegration at zero frequency is invalid, so that prior to any test for cointegration we have to filter the data in such a way that only the pole at the frequency where we suspect the cointegration occurs remains. For instance, if we want to test for cointegration at the origin, we have first to remove seasonal roots, for example by applying the seasonal summation operator, S(L) = (1 + L + · · · + L'- 1), to the original series and then performing a standard cointegration test such as those discussed in Engle and Granger (1987).
