A characterization of cointegrating relationships using induced-order statistics

In this paper we explore the usefulness of induced-order statistics in the characterization of integrated series and of cointegrating relationships. We propose some cointegration testing devices which do not require prior estimation of the cointegration parameter, and therefore lead to null distributions which are free from lluisance parameters. To test the null of non-cointegration, we proposed using the parametric Dickey-Fuller test statistic on a pair of series obtained from the original ones. These series must be cointegrated with cointegration parameter equal to unity whenever the original series are cointegrated. Thus the null distribution of this test is exactly the Dickey-Fuller one, since it does not depend on the estimated regression parameter. We also proposed a pair of non-parametric test statistics for testing the null hypothesis of stationarity of the errors in the regression of two I (1) time series. These tests are powerful against the wide alternative of non-cointegration or ofpaic. of (possibly comoving) 1(0) series. Therefore they do not require prior testing for, unit roots in the senes.