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Title: Inversion copulas from nonlinear state space models Authors:  Worapree Ole Maneesoonthorn - University of Melbourne (Australia) [presenting]
Michael Smith - University of Melbourne (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 likelihood-based methods to estimate the models. To illustrate the breadth of new copulas that can be constructed using our approach, we consider three example latent state space models: a stochastic volatility model with an unobserved component, a Markov switching autoregression, and a Gaussian linear unobserved component model. We use all 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 and density forecasts in every case.