Bayesian multivariate nonlinear state space copula models

A novel flexible class of multivariate nonlinear non-Gaussian state space models, based on copulas, is proposed. Specifically, it is assumed that the observation equation and the state equation are defined by copula families that are not necessarily equal. Inference is performed within the Bayesian framework, using the Hamiltonian Monte Carlo method. Simulation studies show that the proposed copula-based approach is extremely flexible, since it is able to describe a wide range of dependence structures and, at the same time, allows us to deal with missing data. The application to atmospheric pollutant measurement data shows that the approach is suitable for accurate modeling and prediction of data dynamics in the presence of missing values. Comparison to a Gaussian linear state space model and to Bayesian additive regression trees shows the superior performance of the proposed model with respect to predictive accuracy.& COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

This research proposes a novel flexible class of multivariate nonlinear non-Gaussian state space models based on copulas. The observation equation and the state equation are defined by copula families that are not necessarily equal. Inference is performed using the Hamiltonian Monte Carlo method within the Bayesian framework. Simulation studies demonstrate that the copula-based approach is highly flexible, capturing a wide range of dependence structures and enabling handling of missing data. The application to atmospheric pollutant measurement data illustrates the model's suitability for accurate modeling and prediction in the presence of missing values. Comparisons with a Gaussian linear state space model and Bayesian additive regression trees show the superior predictive accuracy of the proposed model.