Highly irregular serial correlation tests

Tests are developed for neglected serial correlation when the information matrix is repeatedly singular under the null hypothesis. Specifically, consideration is given to white noise against a multiplicative seasonal Ar model, and a local-level model against a nesting Ucarimaone. The proposed tests, which involve higher-order derivatives, are asymptotically equivalent to the likelihood ratio test but only require estimation under the null. It is shown that the tests effectively check that certain autocorrelations of the observations are zero, so their asymptotic distribution is standard. Monte Carlo exercises examine finite sample size and power properties, with comparisons made to alternative approaches.