Cointegrated Dynamics for A Generalized Long Memory Process

Recent developments in econometric methods enable estimation and testing of general long memory process, which include the general Gegenbauer process. This paper considers the error correction model for a vector general long memory process, which encompasses the vector autoregressive fractionally-integrated moving average and general Gegenbauer process. We modify the tests for unit roots and cointegration, based on the concept of heterogeneous autoregression.
The Monte Carlo simulations show that the finite sample properties of the modified tests are satisfactory, while the conventional tests suffer from size distortion. Empirical results for interest rates series for the U.S.A. and Australia indicate that:
(1) the modified unit root test detected unit roots for all series,
(2) after differencing, all series favour the general Gegenbauer process,
(3) the modified test for cointegration found only two cointegrating vectors, and
(4) the zero interest rate policy in the U.S.A. has no effect on the cointegrating vector for the two countries