We introduce new dynamic conditional score (DCS) models with time-varyinglocation, scale and shape parameters. For these models, we use the Student's-t, GED(general error distribution), Gen-t (generalized-t), Skew-Gen-t (skewed generalized-t),EGB2 (exponential generalized beta of the second kind) and NIG (normal-inverseGaussian) distributions. We show that the maximum likelihood (ML) estimates of thenew DCS models are consistent and asymptotically Gaussian. As an illustration, weuse daily log-return time series data from the S&P 500 index for period 1950 to 2016.We find that, with respect to goodness-of-fit and predictive performance, the DCSmodels with dynamic shape are superior to the DCS models with constant shape andthe benchmark AR-t-GARCH model
