This paper studies permutation tests for regression parameters in a time series setting, where the time series is assumed stationary but may exhibit an arbitrary (but weak) dependence structure. In such a setting, it is perhaps surprising that permutation tests can offer any type of inference guarantees, since permuting of covariates can destroy its relationship with the response. Indeed, the fundamental assumption of exchangeability of errors required for the finite-sample exactness of permutation tests, can easily fail. However, we show that permutation tests may be constructed which are asymptotically valid for a wide class of stationary processes, but remain exact when exchangeability holds. We also consider the problem of testing for no monotone trend and we construct asymptotically valid permutation tests in this setting as well.

翻译：本文研究时间序列背景下回归参数的置换检验，其中时间序列被假设为平稳的，但可能呈现任意（但较弱）的依赖结构。在此背景下，置换检验能提供某种形式的推断保障或许令人惊讶，因为对协变量进行置换可能会破坏其与响应变量之间的关系。实际上，置换检验在有限样本中精确性所需的误差可交换性基本假设很容易失效。然而，我们证明了可以构造出对一类广泛的平稳过程渐进有效、且在可交换性成立时仍保持精确的置换检验。我们还考虑了无单调趋势的检验问题，并在此背景下构造了渐进有效的置换检验。