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Title: Testing and modelling time series with time varying tails Authors:  Dario Palumbo - Ca' Foscari University of Venice (Italy) [presenting]
Abstract: The occurrence of extreme observations in a time series depends on the heaviness of the tails of its distribution. A dynamic conditional score model (DCS) is proposed for modelling dynamic shape parameters that govern the tail index. The model is based on the Generalised $t$ family of conditional distributions, allowing for the presence of asymmetric tails and therefore the possibility of specifying different dynamics for the left and right tail indices. Both the convergence properties of the model and the implications of the used link functions are examined by simulations. In addition, the size and power properties of a new Lagrange multiplier test to detect the presence of dynamics in the tail index parameter are introduced and studied. The model is fitted to Equity Indices and Credit Default Swaps returns. It is found that the tail index for equities has dynamics driven mainly by the lower tail, whereas for Credit Default Swap the test identifies very persistent dynamics for both the tails. Finally the implications of dynamic tail indices for the estimated conditional distribution are assessed in terms of time-varying quantiles.