This paper proposes an estimator of the cointegrating rank of a potentially cointegrated multivariate fractional process. Our setting is very flexible, allowing the individual observable processes to have different integration orders. The proposed method is automatic and can be also employed to infer the dimensions of possible cointegrating subspaces, which are characterized by special directions in the cointegrating space which generate cointegrating errors with smaller integration orders, increasing the “achievement” of the cointegration analysis. A Monte Carlo experiment of finite sample performance and an empirical analysis are included.

This research is supported by the Spanish Ministerio de Ciencia e Innovación (ref. ECO2008-02641).