A Spatio-Temporal Autoregressive Model for Multi-Unit Residential Market Analysis*

By splitting the spatial effects into building and neighborhood effects, this paper develops a two order spatio-temporal autoregressive model to deal with both the spatio-temporal autocorrelations and the heteroscedasticity problem arising from the nature of multi-unit residential real estate data. The empirical results based on 54,282 condominium transactions in Singapore between 1990 and 1999 show that in the multi-unit residential market, a two order spatio-temporal autoregressive model incorporates more spatial information into the model, thus outperforming the models originally developed in the market for single-family homes. This implies that the specification of a spatio-temporal model should consider the physical market structure as it affects the spatial process. It is found that the Bayesian estimation method can produce more robust coefficients by efficiently detecting and correcting heteroscedasticity, indicating that the Bayesian estimation method is more suitable for estimating a real estate hedonic model than the conventional OLS estimation. It is also found that there is a trade off between the heteroscedastic robustness and the incorporation of spatial information into the model estimation. The model is then used to construct building-specific price indices. The results show that the price indices for different condominiums and the buildings within a condominium do behave differently, especially when compared with the aggregate market indices.This paper was presented at the Singapore–Hong Kong International Real Estate Research Symposium, organized by the Department of Real Estate, National University of Singapore, from 18 to 19 July, 2003.     

Spatial Distribution of Retail Sales

We examine the distribution of sales for a retail chain in the Houston market using a spatial gravity model. Unlike previous empirical studies, our approach models spatial dependencies among both consumers and retailers. The results show that both forms of spatial dependence exert statistically and economically significant impacts on the estimates of parameters in retail gravity models. Contrary to the suggestions of (Gautschi, D. A. (1981). “Specification of Patronage Models for Retail Center Choice,” Journal of Marketing Research 18, 162–174.) as well as (Eppli, M. J., and J. D. Shilling. (1996). “How Critical Is a Good Location to a Regional Shopping Center?” Journal of Real Estate Research 12, 459–468.), our results show the importance of the distance parameter in retail gravity models may be greatly understated. Thus, ignoring spatial dependence may lead to overestimation of the deterministic extent of trade areas, and underestimate the importance of good locations.     

On Spatial Public Finance Empirics

This paper focuses on the empirical specification of theoretical models of strategic interaction that give rise to a spatial pattern in local government expenditures and revenues. It shows that estimation of a reduced form inter-jurisdictional reaction function might not by itself allow to discriminate among competing strategic interaction theories. A review of the recent empirical literature suggests that exploring in more depth the specific empirical implications of alternative theoretical models, as well as fully exploiting the institutional features of multi-tiered government structures and local electoral systems, can help identify the structural model generating the observed spatial auto-correlation in policy variables.JEL Code: H71, H72, H77     

Spatial Dependence and House Price Index Construction

Accurate estimation of prevailing metropolitan housing prices is important for both business and research investigations of housing and mortgage markets. This is typically done by constructing quality-adjusted house price indices from hedonic price regressions for given metropolitan areas. A major limitation of currently available indices is their insensitivity to the geographic location of dwellings within the metropolitan area. Indices are constructed based on models that do not incorporate the underlying spatial structure in housing data sets. In this article, we argue that spatial structure, especially spatial dependence latent in housing data sets, will affect the precision and accuracy of resulting price estimates. We illustrate the importance of spatial dependence in both the specification and estimation of hedonic price models. Assessments are made on the importance of spatial dependence both on parameter estimates and on the accuracy of resulting indices.     

Alternative Models for Describing Spatial Dependence among Dwelling Selling Prices

In this article different spatial statistics techniques to analyze the behavior of used dwelling market prices are compared. We fit two lattice models: simultaneous and conditional autoregressive, a geostatistical model, the so-called universal kriging and finally, a linear mixed-effect model. Different spatial neighborhood structures are considered, as well as different spatial weight matrices and covariance models. The results are illustrated through a real data set of 293 properties from Pamplona, Spain.     

The Predictive Power of Anisotropic Spatial Correlation Modeling in Housing Prices

This paper develops a method to capture anisotropic spatial autocorrelation in the context of the simultaneous autoregressive model. Standard isotropic models assume that spatial correlation is a homogeneous function of distance. This assumption, however, is oversimplified if spatial dependence changes with direction. We thus propose a local anisotropic approach based on non-linear scale-space image processing. We illustrate the methodology by using data on single-family house transactions in Lucas County, Ohio. The empirical results suggest that the anisotropic modeling technique can reduce both in-sample and out-of-sample forecast errors. Moreover, it can easily be applied to other spatial econometric functional and kernel forms.     

Option Pricing Under Autoregressive Random Variance Models

Abstract

The autoregressive random variance (ARV) model introduced by Taylor (1980, 1982, 1986) is a popular version of stochastic volatility (SV) models and a discrete-time simplification of the continuous-time diffusion SV models. This paper introduces a valuation model for options under a discrete-time ARV model with general stock and volatility innovations. It employs the discretetime version of the Esscher transform to determine an equivalent martingale measure under an incomplete market. Various parametric cases of the ARV models, are considered, namely, the log-normal ARV models, the jump-type Poisson ARV models, and the gamma ARV models, and more explicit pricing formulas of a European call option under these parametric cases are provided. A Monte Carlo experiment for some parametric cases is also conducted.     

Spatial modeling of stock market comovements

We model the complex global dependencies in international financial markets using spatial techniques. Our methodology allows us to go beyond conventional correlation analyses and volatility-spillover models confined to studying pairwise relationships, and improves the accuracy of return predictions. We find that stock market comovements are unrelated to geographical proximity, and that financial linkages, as measured by foreign direct investment (FDI) ties, are important in accounting for markets comovements. Our results suggest that the proposed measure of financial distance, coupled with spatial methodology, captures fairly accurately the dependencies in the world financial markets, providing important implications for policymaking and portfolio management.     

Spatial modelling of claim frequency and claim size in non-life insurance

In this paper, models for claim frequency and average claim size in non-life insurance are considered. Both covariates and spatial random effects are included allowing the modelling of a spatial dependency pattern. We assume a Poisson model for the number of claims, while claim size is modelled using a Gamma distribution. However, in contrast to the usual compound Poisson model, we allow for dependencies between claim size and claim frequency. A fully Bayesian approach is followed, parameters are estimated using Markov Chain Monte Carlo (MCMC). The issue of model comparison is thoroughly addressed. Besides the deviance information criterion and the predictive model choice criterion, we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. We give an application to a comprehensive data set from a German car insurance company. The inclusion of spatial effects significantly improves the models for both claim frequency and claim size, and also leads to more accurate predictions of the total claim sizes. Further, we detect significant dependencies between the number of claims and claim size. Both spatial and number of claims effects are interpreted and quantified from an actuarial point of view.     

Spatiotemporal Autoregressive Models of Neighborhood Effects

Using 70,822 observations on housing prices from 1969 to 1991 from Fairfax County Virginia, this article demonstrates the substantial benefits obtained by modeling the spatial as well as the temporal dependence of the data. Specifically, the spatiotemporal autoregression with twelve variables reduced median absolute error by 37.35% relative to an indicator-based model with twenty-six variables. One-step ahead forecasts also document the improved performance of the proposed spatiotemporal model. In addition, the article illustrates techniques for rapidly computing the estimates and shows how to compute indices for any location.