Resuscitating the Co-Fractional Model of Granger

We show that the model for fractional cointegration proposed by Granger (1986) allows for a representation of the solution that demonstrates the fractional and co-fractional properties. Moreover, we show that the stability of the system can be studied by means of the argument principle inherited from complex analysis. As opposed to the FCVARd,b specification of Johansen (2008b), the model is identified for any combination of number of lags and cointegration rank, while being able to generate polynomial co-fractionality. Finally, we characterize the set of recursions to obtain the impulse response functions and we derive the asymptotic theory for the maximum likelihood estimator of the coefficients