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goodness-of-fit tests for multi-dimensional copulas:Expanding application to historical drought data

Water Science and Engineering 2013年第1期6卷 18-30页

作者： Ming-wei MA Li-liang REN Song-bai SONG Jia-li SONG Shan-hu JIANG State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Hohai University College of Water Resources and Architectural Engineering Northwest A&F University Business School Hohai University

The question of how to choose a copula model that best fits a given dataset is a predominant limitation of the copula approach, and the present study aims to investigate the techniques of goodness-of-fit tests for multi-dimensional copulas. A goodness-of-fit test based on Rosenblatt＇s transformation was mathematically expanded from two dimensions to three dimensions and procedures of a bootstrap version of the test were provided. Through stochastic copula simulation, an empirical application of historical drought data at the Lintong Gauge Station shows that the goodness-of-fit tests perform well, revealing that both trivariate Gaussian and Student t copulas are acceptable for modeling the dependence structures of the observed drought duration, severity, and peak. The goodness-of-fit tests for multi-dimensional copulas can provide further support and help a lot in the potential applications of a wider range of copulas to describe the associations of correlated hydrological variables. However, for the application of copulas with the number of dimensions larger than three, more complicated computational efforts as well as exploration and parameterization of corresponding copulas are required.

关键词： goodness-of-fit test, multi-dimensional copulas, stochastic simulation Rosenblatt'stransformation, bootstrap approach," drought data

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