A New Look at Portmanteau Tests

Portmanteau tests are some of the most commonly used statistical methodsfor model diagnostics. They can be applied in model checking either inthe time series or in the regression context. The present paper proposes aportmanteau-type test, based on a sort of likelihood ratio statistic, useful totest general parametric hypotheses inherent to statistical models, which includesthe classical portmanteau tests as special cases. Sufficient conditionsfor the statistic to be asymptotically chi-square distributed are elucidatedin terms of the Fisher information matrix, and the results have very clearimplications for the relationships between the parameter of interest and nuisanceparameter. In addition, the power of the test is investigated when localalternative hypotheses are considered. Some interesting applications of theproposed test to various problems are illustrated, such as serial correlationtests where the proposed test is shown to be asymptotically equivalent toclassical tests. Since portmanteau tests are widely used in many fields, itappears essential to elucidate the fundamental mechanism in a unified view.