A likelihood ratio type test for invertibility in moving average processes

A new test for invertibility of moving average processes is proposed. The test is based on an explicit local approximation of the likelihood ratio. A simulation study compares the power with two previously suggested tests: a score type test and a numerical likelihood ratio test. Local to the null of noninvertibility, the proposed test is seen to have better power properties than the score type test and its power is only slightly below that of the numerical likelihood ratio test. Moreover, the test is extended to an ARMA(p,1) framework, by using it on the estimated residuals of a fitted AR(p) model. A simulation study for ARMA(1, 1) shows that when varying the AR parameter, the test has better size properties than the score type test.