Time series models with an EGB2 conditional distribution

A time series model in which the signal is buried in noise that is non-Gaussian may throw up observations that, when judged by the Gaussian yardstick, are outliers. We describe an observation driven model, based on an exponential generalized beta distribution of the second kind (EGB2), in which the signal is a linear function of past values of the score of the conditional distribution. This specification produces a model that is not only easy to implement, but which also facilitates the development of a comprehensive and relatively straight-forward theory for the asymptotic distribution of the maximum likelihood estimator. The model is fitted to US macroeconomic time series and compared with Gaussian and Student-t models. A theory is then developed for an EGARCH model based on the EGB2 distribution and the model is fitted to exchange rate data. Finally dynamic location and scale models are combined and applied to data on the UK rate of inflation.