We develop a method for long-run predictability testing in series Y by a persistent series X. We consider a class of tests based on the long-run behavior of these series that are robust to short-run dynamics and attempt to attain the highest possible power. The test is based on the Whittle approximation to the likelihood ratio that is adjusted to remain accurate across a range of persistence in X. We verify the properties of this test in small simulations and compare this test against a group of recently proposed methods.

中文翻译：

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使用近乎集成的回归器对长期可预测性进行近乎最优的测试

我们开发了一种通过持久系列 X 在系列 Y 中进行长期可预测性测试的方法。我们考虑基于这些系列的长期行为的一类测试，这些测试对短期动态具有鲁棒性，并试图达到最高可能力量。该测试基于对似然比的 Whittle 近似值，该近似值经过调整以在持续时间范围内保持准确X. 我们在小型模拟中验证了该测试的特性，并将该测试与一组最近提出的方法进行了比较。