Most mean powerful invariant test for testing two-dimensional parameter spaces

This paper investigates the application of the most mean powerful invariant test to the problem of testing for joint MA(1)–MA(4) disturbances against joint AR(1)–AR(4) disturbances in the linear regression model. The most mean powerful invariant test was introduced by Begum and King (Most mean powerful invariant test of a composite null against a composite alternative. Comp. Statist. Data Analysis, 2004, forthcoming) and is based on the generalized Neyman–Pearson lemma which provides an optimal test of certain composite hypotheses. The most mean powerful invariant test can be computationally intensive. Previous applications have only involved testing problems whose null hypotheses, after reduction through invariance arguments, are one dimensional. This is the first application involving null and alternative hypotheses which are two dimensional. A Monte Carlo experiment was conducted to assess the small sample performance of the test with encouraging results. The increase in dimension does increase significantly the computational effort required to apply the test.