Unit root tests based on unconditional maximum likelihood estimation for the autoregressive moving average

Unconditional maximum likelihood estimation is considered for an autoregressive moving average that may contain an autoregressive unit root. The limiting distribution of the normalized maximum likelihood estimator of the unit root is shown to be the same as that of the estimator for the first-order autoregressive process. A likelihood ratio test based on unconditional maximum likelihood estimation is proposed. In a Monte Carlo study for the autoregressive moving-average model of order (1, 1), the new test is shown to have better size and power than those of several other tests.