Fitting MA(q) Models in the Closed Invertible Region
  The use of reparameterization in the maximization of the likelihood function of the MA(q) model is discussed. A general method for testing for the presence of a parameter estimate on the boundary of an MA(q) model is presented. This test is illustrated with a brief simulation experiment for the MA(q) for q=1,2,3,4 in which it is shown that the probability of an estimate being on the boundary increases with q. 
Ying Zhang and A. Ian McLeod
math.ST stat.TH