A geographically and temporally weighted autoregressive model with application to housing prices

Abstract

Spatiotemporal autocorrelation and nonstationarity are two important issues in the modeling of geographical data. Built upon the geographically weighted regression (GWR) model and the geographically and temporally weighted regression (GTWR) model, this article develops a geographically and temporally weighted autoregressive model (GTWAR) to account for both nonstationary and auto-correlated effects simultaneously and formulates a two-stage least squares framework to estimate this model. Compared with the maximum likelihood estimation method, the proposed algorithm that does not require a prespecified distribution can effectively reduce the computation complexity. To demonstrate the efficacy of our model and algorithm, a case study on housing prices in the city of Shenzhen, China, from year 2004 to 2008 is carried out. The results demonstrate that there are substantial benefits in modeling both spatiotemporal nonstationarity and autocorrelation effects simultaneously on housing prices in terms of R² and Akaike Information Criterion (AIC). The proposed model reduces the absolute errors by 31.8% and 67.7% relative to the GTWR and GWR models, respectively, in the Shenzhen data set. Moreover, the GTWAR model improves the goodness-of-fit of the ordinary least squares model and the GTWR model from 0.617 and 0.875 to 0.914 in terms of R². The AIC test corroborates that the improvements made by GTWAR over the GWR and the GTWR models are statistically significant.

Keywords:

• GTWAR
• two-stage least squares estimation
• spatiotemporal nonstationarity
• spatiotemporal autocorrelation
• housing price

Funding

This work was supported in part by the National High-Tech R&D Program (863 Program) through Grant 2009AA122004 and in part by the Hong Kong Research Grants Council through Grant CUHK 444612. Their support is gratefully acknowledged.

Notes

^1. According to Equation (8), we estimate only the impact of previous and current neighboring samples on a current point and the earliest several points are generally not considered. Hence, we use only 400 samples rather than 406 samples.