  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 one 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.
