Cointegrated Dynamics for a Generalized Long Memory Process: Application to Interest Rates

Recent developments in econometric methods enable estimation and testing of general long memory processes, 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 processes. 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 for unit roots are satisfactory, while the conventional tests suffer from size distortion. The experiments also indicate that the modified tests for cointegration improve the problem of finding too many cointegration relationships which arises for fractionally integrated series. Empirical results for interest rates series for the USA 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 (GG) process; (3) the modified test for cointegration found only two cointegrating vectors; and (4) the zero interest rate policy in the USA had no effect on the cointegrating vectors for the two countries.

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