Paolo Santucci de Magistris (LUISS)

with Federico Carlini

We study the theoretical properties of the model for fractional cointegration proposed by Granger (1986). We show that the stability of discrete-time stochastic systems of the type Pi(L)Yt= epsilont can be assessed with the argument principle. We demonstrate that the model admits a Granger representation and a closed-form expression for the impulse response functions. We prove that the model is identified for any combination of number of lags and cointegration rank. We prove that the properties of the maximum likelihood estimator reconcile with those of the FCVAR model studied in Johansen and Nielsen (2012). Finally, we provide an empirical illustration of the proposed model to study the dynamic relation between realized and implied variance.