  This paper investigates the (conditional) quasi-likelihood ratio test for the
threshold in MA models. Under the hypothesis of no threshold, it is shown that
the test statistic converges weakly to a function of the centred Gaussian
process. Under local alternatives, it is shown that this test has nontrivial
asymptotic power. The results are based on a new weak convergence of a linear
marked empirical process, which is independently of interest. This paper also
gives an invertible expansion of the threshold MA models.
