In testing for correlation of the errors in regression models, the power of tests can be very low for strongly correlated errors. This counterintuitive phenomenon has become known as the “zero-power trap.” Despite a considerable amount of literature devoted to this problem, mainly focusing on its detection, a convincing solution has not yet been found. In this article, we first discuss theoretical results concerning the occurrence of the zero-power trap phenomenon. Then, we suggest and compare three ways to avoid it. Given an initial test that suffers from the zero-power trap, the method we recommend for practice leads to a modified test whose power converges to $1$ as the correlation gets very strong. Furthermore, the modified test has approximately the same power function as the initial test and thus approximately preserves all of its optimality properties. We also provide some numerical illustrations in the context of testing for network generated correlation.

在测试回归模型中误差的相关性时，对于强相关误差，测试的功效可能非常低。这种违反直觉的现象被称为“零功率陷阱”。尽管有大量文献致力于这个问题，主要集中在其检测上，但尚未找到令人信服的解决方案。在本文中，我们首先讨论有关零功率陷阱现象发生的理论结果。然后，我们建议并比较三种避免这种情况的方法。给定一个遭受零功效陷阱的初始测试，我们推荐的实践方法会导致修改后的测试，随着相关性变得非常强，其功效收敛到1$。此外，修改后的测试具有与初始测试大致相同的幂函数，因此大致保留了其所有最优性属性。我们还在测试网络生成的相关性的背景下提供了一些数值说明。