Testing and modelling time varying (a)symmetric tails

The occurrence of extreme observations in a time series depends on the heaviness of the distribution’s tails. This paper proposes a score-driven framework for detecting and modelling time-varying tail behaviour. The framework is based on the t conditional distributions and is extended to allow for asymmetric tails with distinct dynamic behaviour. In addition, the paper introduces a novel Lagrange Multiplier test to detect the presence of dynamics in the tail index parameters. The paper examines the properties of the test and demonstrates that it is more effective than existing methodologies at detecting tail variation. The framework is then applied to the tail behaviour of market returns from Equity Indices and Credit Default Swaps. The implications of neglecting dynamic tail features are assessed in terms of conditional density forecasts. The paper shows that allowing for a dynamic tail index, where appropriate, improves the forecasting accuracy of expected shortfalls and value-at-risk.