  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.
