Time series models with infinite-order partial copula dependence

TL;DR

This paper introduces a new class of infinite-order partial copula dependence models for time series, extending classical linear processes to non-Gaussian and more flexible dependence structures, with practical parameterization methods and applications.

Contribution

It generalizes Gaussian ARMA and ARFIMA models to infinite copula sequences, allowing non-Gaussian marginals and dependence, with new parameterization techniques and applications.

Findings

Models can better fit macroeconomic data.

Extension of classical linear processes to copula-based models.

Practical parameterization using Kendall partial autocorrelation.

Abstract

Stationary and ergodic time series can be constructed using an s-vine decomposition based on sets of bivariate copula functions. The extension of such processes to infinite copula sequences is considered and shown to yield a rich class of models that generalizes Gaussian ARMA and ARFIMA processes to allow both non-Gaussian marginal behaviour and a non-Gaussian description of the serial partial dependence structure. Extensions of classical causal and invertible representations of linear processes to general s-vine processes are proposed and investigated. A practical and parsimonious method for parameterizing s-vine processes using the Kendall partial autocorrelation function is developed. The potential of the resulting models to give improved statistical fits in many applications is indicated with an example using macroeconomic data.