On the Identification of Fractionally Cointegrated VAR Models With theF(d)Condition
研究了分整协整VAR模型中参数识别问题，给出了一个称为F(d)的充要条件，并说明协整秩与滞后阶数之间存在不可区分性。
This article discusses identification problems in the fractionally cointegrated system of Johansen and Johansen and Nielsen. It is shown that several equivalent reparametrizations of the model associated with different fractional integration and cointegration parameters may exist for any choice of the lag-length when the true cointegration rank is known. The properties of these multiple nonidentified 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). This is a generalization of the well-known I(1) condition to the fractional case. Imposing a proper restriction on the fractional integration parameter, d, is sufficient to guarantee identification of all model parameters and the validity of the F(d) condition. The article also illustrates the indeterminacy between the cointegration rank and the lag-length. It is also proved that the model with rank zero and k lags may be an equivalent reparameterization of the model with full rank and k − 1 lags. This precludes the possibility to test for the cointegration rank unless a proper restriction on the fractional integration parameter is imposed.