A method for spatial-temporal forecasting with an application to real estate prices
Using 5243 housing price observations during 1984-92 from Baton Rouge, this manuscript demonstrates the substantial benefits obtained by modeling the spatial as well as the temporal dependence of the errors. Specifically, the spatial-temporal autoregression with 14 variables produced 46.9% less SSE than a 12-variable regression using simple indicator variables for time. More impressively, the spatial-temporal regression with 14 variables displayed 8% lower SSE than a regression using 211 variables attempting to control for the housing characteristics, time, and space via continuous and indicator variables. One-step ahead forecasts document the utility of the proposed spatial-temporal model. In addition, the manuscript illustrates techniques for rapidly computing the estimates based upon an interesting decomposition for modeling spatial and temporal effects. The decomposition maximizes the use of sparsity in some of the matrices and consequently accelerates computations. In fact, the model uses the frequent transactions in the housing market to help simplify computations. The techniques employed also have applications to other dimensions and metrics.