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Article
Modeling Longitudinal Data using a Pair-Copula Decomposition of Serial Dependence
Journal of the American Statistical Association (2010)
  • Michael S Smith, Melbourne Business School
  • Aleksey Min
  • Carlos Almeida
  • Claudia Czado
Abstract

Copulas have proven to be very successful tools for the flexible modelling 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 out-performs 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.

Keywords
  • Longitudinal Copulas,
  • Covariance Selection,
  • Inhomogenous Markov Process,
  • D-vine,
  • Bayesian Model Selection,
  • Goodness of Fit,
  • Intraday Electricity Load
Publication Date
December, 2010
Citation Information
Michael S Smith, Aleksey Min, Carlos Almeida and Claudia Czado. "Modeling Longitudinal Data using a Pair-Copula Decomposition of Serial Dependence" Journal of the American Statistical Association Vol. 105 Iss. 492 (2010)
Available at: http://works.bepress.com/michael_smith/23/