Modeling Longitudinal Data Using a Pair-Copula Decomposition of Serial Dependence

• 成果类型: Article
• 署名作者: Smith, Michael; Min, Aleksey; Almeida, Carlos; Czado, Claudia
• 署名单位: University of Melbourne; Technical University of Munich
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2010.tm09572
• 发表日期: 2010
• 页码: 1467-1479
• 关键词: selection; distributions; association; inference

摘要

Copulas have proven to be very successful tools for the flexible modeling of cross-sectional dependence. In this paper we express the dependence structure of continuous-valued time series data using a sequence of bivariate copulas. This corresponds to a type of decomposition recently called a vine in the graphical models literature, where each copula is entitled a pair-copula. We propose a Bayesian approach for the estimation of this dependence structure for longitudinal data. Bayesian selection ideas are used to identify any independence pair-copulas, with the end result being a parsimonious representation of a time-inhomogeneous Markov process of varying order. Estimates are Bayesian model averages over the distribution of the lag structure of the Markov process. Using a simulation study we show that the selection approach is reliable and can improve the estimates of both conditional and unconditional pairwise dependencies substantially. We also show that a vine with selection outperforms a Gaussian copula with a flexible correlation matrix. The advantage of the pair-copula formulation is further demonstrated using a longitudinal model of intraday electricity load. Using Gaussian, Gumbel, and Clayton pair-copulas we identify parsimonious decompositions of intraday serial dependence, which improve the accuracy of intraday load forecasts. We also propose a new diagnostic for measuring the goodness of fit of high-dimensional multivariate copulas. Overall, the pair-copula model is very general and the Bayesian method generalizes many previous approaches for the analysis of longitudinal data. Supplemental materials for the article are also available online.