In this work, which is based on the family of Fractional Iterated Ornstein Uhlenbeck processes, we propose a new hypothesis test to contrast short memory versus long memory in time series. This family includes short memory and long memory processes, and has the ability to approximate a long memory processes by a short memory processes. Based on the asymptotic results of the estimators of its parameters, we will present the test and show how it can be implemented. Also, we will show a comparison with other tests widely used under both short memory and long memory scenarios. The main conclusion is that this new test is the one with best performance under the null hypothesis, and has the maximum power in some alternatives.

翻译：在这项工作中,我们基于分形迭代 Ornstein Uhlenbeck 程序,提出了一个新的假设测试,以对比短记忆和长记忆在时间序列中的对比。这个模型包括短记忆和长记忆过程,并且能够以短记忆过程来近似长记忆过程。根据测算参数的零时间结果,我们将展示测试并展示如何实施。此外,我们将展示与其他在短记忆和长记忆情景下广泛使用的其他测试的比较。主要结论是,这个新测试在无效假设下表现最佳,在某些替代方案下具有最大能力。