We consider borrowing information over time in small area estimation (SAE) in the setting of area level modeling of repeated survey estimates for a small number of time points for a moderate to large number of areas. Previous work on this topic has tended to focus on one of three related models: the first order autoregressive (AR(1)) model, the random walk model, and a model of Rao and Yu (1994) that adds to the AR(1) model a time constant area level random effect. The heavy focus on this limited set of time series models in the SAE literature leaves open questions about how the three models compare, whether alternative time series models may fit better in given applications, and to what extent such alternative models may improve small area predictions. We investigate these questions here by proposing for SAE use of the autoregressive-integrated-moving average (ARIMA) models originally proposed by Box and Jenkins. The SAE setting of modeling repeated survey estimates with sampling error that are assumed independent cross-sectionally but dependent over time requires modifications to the approach of Box and Jenkins for model identification/selection and how estimation and prediction are performed. We thus propose a framework that adapts the ARIMA modeling approach to the SAE setting and incorporates a generalization of the Rao-Yu AR(1) model. Our framework draws a simple but important distinction, often ignored, between homogeneous and heterogeneous models. The former assumes regression parameters and variances are constant over time, while the latter lets these be different for different time points. We demonstrate use of this framework via detailed analysis of two examples, using a Bayesian approach implemented with the JAGS software. Results for the examples show the commonly used AR(1), random walk, and Rao-Yu AR(1) models generally performed worse than some of the alternative models considered.