Tests of Seasonal and Non-Seasonal Serial Correlation

This paper considers tests for seasonal and non-seasonal serial correlation in time series and in the errors of regression models. The problem of testing for white noise against multiplicative seasonal ARMA(l,l)-ARMA(l,l) alternatives is investigated. This testing problem is non-standard due to nuisance parameters that appear under the alternative but not under the null hypothesis. The likelihood ratio (LR), sup Lagrange multiplier (LM), and exponential average LM and LR tests are considered and are shown to be asymptotically admissible for multiplicative seasonal ARMA(l,l)-ARMA(l,l) alternatives. In addition, they are shown to be consistent against all (weakly stationary strong mixing) non-white noise alternatives. Simulation results compare the tests to several tests in the literature. The exponential average test, Exp-LRinfinity, is found to be the best test overall. It performs substantially better than the Box-Pierce, Durbin-Watson, and Wallis tests.