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

Stefan Birr, Tobias Kley, Stanislav Volgushev*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

7 Citations (Scopus)
53 Downloads (Pure)


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 nonlinear 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.
Original languageEnglish
Pages (from-to)122-146
Number of pages25
JournalJournal of Multivariate Analysis
Issue number209
Early online date18 Mar 2019
Publication statusPublished - 1 Jul 2019


  • Copula
  • time series
  • bootstrap
  • spectral density
  • frequency domain


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