Paolo Gorgi, Vrije Universiteit Amsterdam

"Conditional score residuals and diagnostic analysis of serial dependence in time series models"

Abstract

We introduce a general framework for diagnostic analysis of time series models that relies on the definition of conditional score residuals. Conditional score residuals encompass standard definitions of residuals that are typically used in time series models. ARMA residuals, squared residuals and Pearson residuals are special cases of conditional score residuals when the conditional distribution of the model belongs to the exponential family. Instead, conditional score residuals provide an alternative definition of residuals when the conditional distribution is not of the exponential type. The asymptotic properties of empirical autocorrelation functions of conditional score residuals are formally derived for a wide class of time series models. The results yield a unified theory for diagnostic analysis of observation-driven time series models. A key feature of conditional score residuals is that they account for the shape of the conditional distribution. This produces more reliable and powerful diagnostic tools for testing residual autocorrelation. Furthermore, they can also be employed in complex models where it may not be clear how to define residuals. We illustrate the practical relevance of the proposed framework by considering two examples that feature a heavy-tailed GARCH model and a dynamic copula model. A simulation study and an empirical application to the returns of the S&P500 index show how squared residuals are not reliable in testing residual autocorrelation in GARCH models with extreme observations. Instead, conditional score residuals are robust to outliers and they provide more powerful diagnostic tools.

Co-authors: F. Blasques and S.J. Koopman

Contact person: Stefan Voigt