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

Author

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  • Birr, Stefan
  • Kley, Tobias
  • Volgushev, Stanislav

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 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.

Suggested Citation

  • Birr, Stefan & Kley, Tobias & Volgushev, Stanislav, 2019. "Model assessment for time series dynamics using copula spectral densities: A graphical tool," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 122-146.
    • Handle: RePEc:eee:jmvana:v:172:y:2019:i:c:p:122-146
    DOI: 10.1016/j.jmva.2019.03.003
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    Cited by:

    1. Yuichi Goto & Tobias Kley & Ria Van Hecke & Stanislav Volgushev & Holger Dette & Marc Hallin, 2021. "The Integrated Copula Spectrum," Working Papers ECARES 2021-29, ULB -- Universite Libre de Bruxelles.
    2. Chen, Tianbo & Sun, Ying & Li, Ta-Hsin, 2021. "A semi-parametric estimation method for the quantile spectrum with an application to earthquake classification using convolutional neural network," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).

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