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In this paper we introduce new Dynamic Conditional Score (DCS) models for the Skew-Gen-t (Skewed Generalizedt) and NIG(Normal-Inverse Gaussian) distributions as alternatives to the recent DCS models for the Student’s-t and EGB2 (Exponential Generalized Beta of the second kind) distributions, respectively. The DCS models we propose include stochastic local level, stochastic seasonality, and irregular components with DCS-EGARCH (Exponential Generalized Autoregressive Conditional Heteroscedasticity) volatility dynamics. DCS models are robust to extreme observations, whereas standard financial time series models are not. We use data from the Guatemalan Quetzal (GTQ) to United States Dollar (USD) exchange rate for the period of 4th January 1994–30th June 2017. This dataset exhibits significant rises and falls in the GTQ/USD that lead to extreme observations, stochastic seasonality with dynamic amplitude, and volatility dynamics. These seasonality dynamics of the GTQ/USD are related to the Guatemalan trade-related currency movements, receipt and payment of foreign loans, and remittance payments of Guatemalans working abroad. We show that the in-sample statistical performance of the DCS-Skew-Gen-t and the DCS-NIG models is superior to that of the DCS-t and the DCS-EGB2 models, respectively. Furthermore, we show that the statistical performance of all DCS models is superior to that of the standard financial time series model.
