A note on the identification and preliminary estimation of MA models

In this paper, we examine some problems that the sampling fluctuation of the estimated autocorrelation function causes in the identification and preliminary estimation of a first order Moving Average model. We reconsider the idea that the identification criterion, based on the approximate confidence limits around the estimated autocorrelation function, could restrict the theoretical parametric space, where the process is defined. In particular, we evaluate approximately the probability that a MA process can be correctly identified by using that criterior. Furthermore, we consider the moment estimator of q and ,with a similar approach, we compute the probability that this estimator provides estimates out of the invertibility region. A simulation study which confirms the theoretical results concludes the paper