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Unformatted text preview: Copula Models for Spatial Point Patterns and Processes Todd H. Kuethe * Todd Hubbs Brigitte Waldorf Current Draft: May 11, 2009 c Abstract This paper presents a new methodological approach for modeling continuous point-generating pro- cesses leading to spatial point patterns. It explores the theoretical foundation and potential applications for copula models in spatial sciences. A copula is a function that combines univariate distributions to obtain a joint distribution with a particular dependence structure. The method is flexible because it separates the choice of dependence among variables from the choice of the marginal distributions of each variable. In addition, copulas are powerful because they are able to capture dependence structures in extreme distributions and in the tails of a distribution. Copula techniques are well established in both financial econometrics and actuarial science, yet the potential of copulas in the context of spatial sciences is relatively unexplored. The study includes an application of spatial copulas to model housing values in an urban area, using complex components such as distance decay, directionality, and edge effects. Keywords: copula methods, spatial analysis, joint dependence JEL Codes: C31, R12 * Corresponding author: email@example.com The authors wish to thank Raymond Florax for helpful comments on a previous draft of this paper. All remaining errors are our own. 1 Introduction This paper presents a new methodological approach for modeling continuous point-generating processes leading to spatial point patterns. There are a number of spatial process models developed in recent years to address the effects of spatial dependence in regression analysis, as well as, models developed to interpolate and predict outcomes in space (see Anselin, 2001). These methods are predominately limited to modeling univariate or multivariate distributions in a conditional probability framework. That is, they model the data generating process of random variables given the occurrence of a set of explanatory variables. The focus of this study however is modeling the data generating process of multiple jointly determined variables in space, free of conditional probability assumptions. Multivariate models are often difficult to estimate in applied work due to complex nonlinearities and nonnormal behavior in observed data, and the modeling of spatial processes is no exception. We attempt to show that researchers can easily draw from current tools for modeling conditional spatial processes to model joint distributions across a geographic space through copula methods. Copula methods provide a set of tools for modeling joint distributions which require only a limited set of information related to univariate marginal distributions and a measure of dependence between variables....
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08