Maximum likelihood estimation, in most ways the best procedure, involves a large amount of computational effort so that two approximate techniques, exact least squares and conditional 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. The STARMA model family is useful in modeling time histories of spatially located data. These models incorporate a hierarchical definition of spatial order with respect to lagged values of both the independent variable and lagged values of the innovations. Formulas, tables, and eight references are included. (Author abstract modified)