In the following we examine, compare, and to a point, advocate simple methods of spacio-temporal description and forecasting. Included are the two-level state-space system, and time-varying parameter least squares auto-regressive system, along with their respective solving algorithms, the Kalman Filter, and auto-regressive Adaptive Least Squares (ALS). Advantages especially attributed to ALS include computational frugality, ease of implementation and interpretation, broad applicability, flexibility, and often excellent performance. Additionally, since ALS relies on estimating response covariation, it may also serve as a precursor to space-time interpolation where specification of a covariogram is required. Comparisons on several contrived datasets and three real datasets included.