Model assessment for time series dynamics using copula spectral densities: a graphical tool

TL;DR

This paper introduces a new graphical tool based on copula spectral densities for assessing the dependence structure in time series, especially capturing non-linear dynamics beyond traditional covariance-based methods.

Contribution

It proposes a novel, theoretically justified graphical approach using copula spectral densities to evaluate time series models' ability to capture complex dependencies.

Findings

Successfully distinguishes subtle differences in time series dynamics.

Effectively detects non-linear dependencies in GARCH and EGARCH models.

Demonstrates practical utility with S&P 500 return data.

Abstract

Finding parametric models that accurately describe the dependence structure of observed data is a central task in the analysis of time series. Classical frequency domain methods provide a popular set of tools for fitting and diagnostics of time series models, but their applicability is seriously impacted by the limitations of covariances as a measure of dependence. Motivated by recent developments of frequency domain methods that are based on copulas instead of covariances, we propose a novel graphical tool that allows to access the quality of time series models for describing dependencies that go beyond linearity. We provide a thorough theoretical justification of our approach and show in simulations that it can successfully distinguish between subtle differences of time series dynamics, including non-linear dynamics which result from GARCH and EGARCH models. We also demonstrate the utility of the proposed tools through an application to modeling returns of the S&P 500 stock market index.