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Title: Inversion copulas from nonlinear state space models Authors:  Michael Smith - University of Melbourne (Australia) [presenting]
Worapree Ole Maneesoonthorn - Monash University (Australia)
Abstract: While copulas constructed from inverting latent elliptical, or skew-elliptical, distributions are popular, they can be inadequate models of serial dependence in time series. As an alternative, we propose an approach to construct copulas from the inversion of latent nonlinear state space models. This allows for new time series copula models that have the same serial dependence structure as a state space model, yet have an arbitrary marginal distribution something that is difficult to achieve using other time series models. We examine the time series properties of the copula models, outline measures of serial dependence, and show how to use Bayesian methods to estimate the models. To illustrate the breadth of new copulas that can be constructed using our approach, we consider example latent state space models. We use the resulting three inversion copulas to model and forecast quarterly U.S. inflation data. We show how combining the serial dependence structure of the state space models, with flexible asymmetric and heavy-tailed margins, improves the accuracy of the fit substantially.