The purpose of this study was to evaluate the robustness of estimated growth curve models when there is stationary autocorrelation among manifest variable errors. The results suggest that when, in practice, growth curve models are fitted to longitudinal data, alternative rival hypotheses to consider would include growth models that also specify autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA) processes. AR (i.e., simplex) processes are commonly found in longitudinal data and may diminish the ability of a researcher to detect growth if not explicitly modeled. MA and ARMA processes do not affect the fit of growth models, but do notably bias some of the parameters.