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

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 to assess the quality of time series models for describing dependencies that go beyond linearity. We provide a theoretical justification of our approach and show in simulations that it can successfully distinguish between subtle differences in 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. (C) 2019 Elsevier Inc. All rights reserved.