Geostatistical space–time mapping of house prices using Bayesian maximum entropy

ABSTRACT

Mapping spatial processes at a small scale is a challenge when observed data are not abundant. The article examines the residential housing market in Fort Worth, Texas, and builds price indices at the inter- and intra-neighborhood levels. To accomplish our objectives, we initially model price variability in the joint space–time continuum. We then use geostatistics to predict and map monthly housing prices across the area of interest over a period of 4 years. For this analysis, we introduce the Bayesian maximum entropy (BME) method into real estate research. We use BME because it rigorously integrates uncertain or secondary soft data, which are needed to build the price indices. The soft data in our analysis are property tax values, which are plentiful, publicly available, and highly correlated with transaction prices. The results demonstrate how the use of the soft data provides the ability to map house prices within a small areal unit such as a subdivision or neighborhood.

KEYWORDS:

• Spatiotemporal
• geostatistics
• kriging
• Bayesian maximum entropy
• real estate

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental data

Supplemental data for this article can be accessed here.

Notes

1. Journel (1989), Goovaerts (1997), and Chilès and Delfiner (1999) provide good starting points to understand geostatistics and the kriging family of techniques.

2. See Christakos (2000) for an extensive review of BME, and also in Christakos (2010, 2014) for conceptual perspectives of BME mapping in the context of critical reasoning and logic. Spatiotemporal BME has been applied in numerous studies and disciplines that illustrate its advantages and improvements (Yu et al. 2015). See examples in the fields of environmental and air pollution in Kolovos et al. (2002, 2010), disease modeling in Angulo et al. (2013), and renewable resources in Zagouras et al. (2015).

3. BME addresses other issues mentioned in the real estate literature. For instance, Pinkse and Slade (2010) noted that the normality assumption, endogeneity, and nonlinearity in the variable behavior cause significant challenges for the hedonic methods. BME makes no assumptions regarding the underlying data distribution and the predictor. Helbich (2015) is another example of spatial modeling that mitigates some of the issues of the spatial weight matrix. He uses fuzzy clustering and generalized additive hedonic model, the latter of which allows for nonlinear effects between the regressand and independent variables.

4. For our analysis, we use the BMElib library (Christakos et al. 2002) on Mathworks® Matlab. We performed the numerical tasks on an Intel® 6-core i7 desktop running Linux operating system at 4.2 GHz. BMElib is available in BME/kriging software (Yu et al. 2007) free of charge at http://seksgui.org.

5. Tarrant County makes new assessments values publicly available at the end of each calendar year. Our method thus considers the tax assessed values as available to BME in the January of the following year. This is a sensible modeling perspective because it reflects the realistic situation that the assessment data are available to the entire market at the same time.

6. The Federal Housing Finance Administration produces price values for smaller cities down to populations of 10,000; however, to build these values, they use appraisal data. The appraisal data suffer from the same uncertainty and issues as the soft data we described in the preceding subsection.

7. Animations of the entire 48-month period (January 2009–December 2012) of predicted transaction prices are available as supplementary files on the journal website. See ‘mov1a-AbmePred.gif’ for BME and ‘mov1b-AkrigPred.gif’ for kriging.

8. Animation of the entire 48-month period (January 2009–December 2012) of predicted transaction prices is available as the supplementary file ‘mov2-BbmeSmallPred.gif’ on the journal website.