On the identification of fractionally cointegrated VAR models with the F(d) condition

This paper discusses identification problems in the fractionally cointegrated system of Johansen (2008) and Johansen and Nielsen (2012). The identification problem arises when the lag structure is over-specified, such that there exist several equivalent reparametrization of the model associated with different fractional integration and cointegration parameters. The properties of these multiple non-identified sub-models are studied and a necessary and sufficient condition for the identification of the fractional parameters of the system is provided. The condition is named F(d). The assessment of the F(d) condition in the empirical analysis is relevant for the determination of the fractional parameters as well as the lag structure.