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，其中时间序列被假定为平稳的，但可能呈现出任意（但较弱的）依赖结构。在这样的设定下，由于对协变量进行置换可能会破坏其与响应变量之间的关系，置换检验能够提供任何形式的推断保证或许令人惊讶。事实上，置换检验在有限样本下精确性所需的误差可交换性这一基本假设可能很容易失效。然而，我们证明了对于一大类平稳过程，可以构造出渐近有效的置换检验，并且当可交换性成立时这些检验仍然保持精确性。我们还考虑了无单调趋势的检验问题，并在此设定下同样构造了渐近有效的置换检验。