Modelling Longitudinal Data using a Pair-Copula Decomposition of Serial Dependence
by Professor Michael Smith
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 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. Overall, the pair-copula construction is very general and the Bayesian approach generalises many previous methods for the analysis of longitudinal data. Both the reliability of the proposed Bayesian methodology, and the advantages of the pair-copula formulation, are demonstrated via simulation and two examples. The first is an agricultural science example, while the second is an econometric model for the forecasting of intraday electricity load. For both examples the Bayesian pair-copula model is substantially more flexible than longitudinal models employed previously.
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