Non-Linear Time Series Modelling and Distributional Flexibility

Most of the existing work in non-linear time series analysis has concentrated on generating flexible functional models by specifying non-linear specifications for the mean of a particular process without much, if any, attention given to the distributional properties of the model. However, as Martin (1991) has shown, greater flexibility in perhaps a more natural way, can be achieved by consideration of distributions from the generalized exponential class. This paper represents an extension of the earlier work of Martin by introducing a flexible class of non-linear time series models which can capture a wide range of empirical behaviour such as skewed, fat-tailed .and even multimodal distributions. This class of models is referred to as GENTS: Generalized Exponential Non-linear Time Series. A maximum likelihood algorithm is given for estimating the parameters of the model, and the framework is applied to estimating the distribution of the movements of the exchange rate.