Spatial models for real estate valuation

The academic and professional literature has, with few exceptions, not explored the use of spatial information for purposes of predicting real estate prices on a local scale. In this paper, we present and analyze several techniques for exploring and estimating spatial structure and for predicting sale price based on location. We demonstrate the usefulness of these techniques by subjecting an extensive real estate data set to a predictive analysis.; We start by discussing the basic nature of spatial covariation and how these concepts relate to the analysis of real estate valuation. We describe how to properly construct a spatial correlogram and avoid some of the pitfalls in the literature resulting from the time series bias which generally assumes gridded data and precludes true 2-dimensional isotropy. We also develop a framework for analyzing and presenting the important likelihood relationships among the multiple parameters in a basic spatial model. We discuss the problems inherent in this framework and in the use of the multivariate normal probability distribution in this context.; We use these techniques to explore the spatial structure in a sample data set of over 8,000 records of real estate transactions from 1986 to 1995 in a small section of Los Angeles. This reveals significant, substantial and stable spatial structure for the first half of our study period, and we discuss various aspects of this structure. We also discuss the emergence of an outlier process in the second half of our study period which dominates any spatial structure that might be there. We propose an explanation for this outlier process which utilizes a statistic we describe as a "spatial information" measure. We present some preliminary empirical findings supporting this framework.; For prediction, we compare several techniques, including kriging and cokriging which we borrow from the geostatistics field. We discuss modelling and computational aspects of these techniques and pay special attention to the issue of local versus global validity of the predictive model assumptions. Additionally, we focus on techniques that would allow us to utilize covariate-only observations in our data set. These techniques potentially allow us to include much more information in our predictive procedure than conventional techniques because we have many more covariate-only observations (e.g. observations of only lot/building size) than variate/covariate observations (e.g. lot/building-size and sales price). We discuss how our knowledge of their spatial distribution allows us to utilize this information predictively and we discuss the modelling and computational problems associated with these techniques. In particular, we present several results relating-kriging and cokriging solutions and how these results direct our modelling of the joint spatial covariance function of the model variables.