NON‐LINEAR TIME SERIES MODELLING AND DISTRIBUTIONAL FLEXIBILITY

Abstract. 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 (J. Time Ser. Anal. 13 (1992), 79–94) 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 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.

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