A simulation experiment compares the accuracy and precision of three alternate estimation techniques for the parameters of the STARMA model. Maximum likelihood estimation, in most ways the "best" estimation procedure, involves a large amount of computational effort so that two approximate techniques, exact least squares and conditional maximum likelihood, are often proposed for series of moderate lengths. This simulation experiment compares the accuracy of these three estimation procedures for simulated series of various lengths, and discusses the appropriateness of the three procedures as a function of the length of the observed series.