How to avoid the zeropower trap in testing for correlation
Abstract
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 "zeropower 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 zeropower trap phenomenon. Then, we suggest and compare three ways to avoid it. Given an initial test that suffers from the zeropower 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2018
 arXiv:
 arXiv:1812.10752
 Bibcode:
 2018arXiv181210752P
 Keywords:

 Mathematics  Statistics Theory;
 Economics  Econometrics;
 Statistics  Methodology