Stationary vine copula models for multivariate time series

Multivariate time series exhibit two types of dependence: across variables and across time points. Vine copulas are graphical models for the dependence and can conveniently capture both types of dependence in the same model. We derive the maximal class of graph structures that guarantee stationarity under a natural and verifiable condition called translation invariance. We propose computationally efficient methods for estimation, simulation, prediction, and uncertainty quantification and show their validity by asymptotic results and simulations. The theoretical results allow for misspecified models and, even when specialized to the iid case, go beyond what is available in the literature. The new model class is illustrated by an application to forecasting returns of a portfolio of 20 stocks, where they show excellent forecast performance. The paper is accompanied by an open source software implementation. (C) 2022 The Author(s). Published by Elsevier B.V.

Automated summary

This paper introduces a graphical model using vine copulas to capture both types of dependence in multivariate time series, i.e., across variables and across time points. The maximal class of graph structures that ensure stationarity under the condition of translation invariance is derived. The paper proposes efficient methods for estimation, simulation, prediction, and uncertainty quantification, and verifies their validity through asymptotic results and simulations. The new model class demonstrates excellent forecast performance in predicting the returns of a portfolio of 20 stocks and is accompanied by open source software implementation.