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Finding parametric models that accurately describe the dependence structureof observed data is a central task in the analysis of time series. Classicalfrequency domain methods provide a popular set of tools for fitting anddiagnostics of time series models, but their applicability is seriouslyimpacted by the limitations of covariances as a measure of dependence.Motivated by recent developments of frequency domain methods that are based oncopulas instead of covariances, we propose a novel graphical tool that allowsto access the quality of time series models for describing dependencies that gobeyond linearity. We provide a thorough theoretical justification of ourapproach and show in simulations that it can successfully distinguish betweensubtle differences of time series dynamics, including non-linear dynamics whichresult from GARCH and EGARCH models. We also demonstrate the utility of theproposed tools through an application to modeling returns of the S&P 500 stockmarket index.

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