Extremal Dependence-Based Specification Testing of Time Series

We propose a specification test for conditional location--scale models based on extremal dependence properties of the standardized residuals. do so comparing left-over serial -- as measured by pre-asymptotic tail copula with that arising under independence at different lags. Our main theoretical results show proposed Portmanteau-type statistics have nuisance parameter-free asymptotic limits. The are easy to compute, they only depend residuals, and critical values likewise easily obtained from limiting distributions. This contrasts extant tests (based, e.g., autocorrelations squared residuals), where parameter estimator model may need be bootstrapped. our performs well in simulations. An empirical application S&P 500 constituents illustrates can uncover violations residual not picked up standard autocorrelation-based tests, yet relevant when is used for, risk forecasting.