Stationary vine copula models for multivariate time series

TL;DR

This paper introduces stationary vine copula models for multivariate time series, providing new theoretical insights, estimation methods, and an application to stock return forecasting, with open source software available.

Contribution

It derives the maximal class of stationary vine copula models under translation invariance and develops efficient estimation and prediction methods with theoretical guarantees.

Findings

Excellent forecast performance in stock return application

Asymptotic validity of estimation methods

Theoretical advancements for misspecified models

Abstract

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. Their proofs are based on new results for general semiparametric method-of-moment estimators, which shall be of independent interest. 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.