Abstract 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.

中文翻译：

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广义长记忆过程的协整动力学：应用于利率

摘要计量经济学方法的最新发展使得能够估计和测试一般的长记忆过程，包括一般的Gegenbauer过程。本文考虑了向量一般长存储过程的纠错模型，该模型包括向量自回归分数积分移动平均值和一般Gegenbauer过程。我们基于异类自回归的概念修改单元根和协整的测试。蒙特卡罗模拟表明，改进的单位根检验的有限样本属性令人满意，而常规检验的尺寸失真。实验还表明，改进的协整检验改善了发现分数积分级数过多的协整关系的问题。美国和澳大利亚利率系列的经验结果表明：（1）修改后的单位根检验可以检测所有系列的单位根；（2）求异后，所有系列都倾向于一般的Gegenbauer（GG）工艺；（3）改进的协整检验发现只有两个协整向量；（4）美国的零利率政策对两国的协整向量没有影响。