Generalized structural time series model
A new class of univariate time series models is developed, the Generalized Structural (GEST) time series model. The GEST model extends Gaussian structural time series models by allowing the distribution of the dependent variable to come from any parametric distribution, including highly skew and=or kurtotic distributions. Furthermore, the GEST model expands the systematic part of time series models to allow the explicit modelling of any or all of the distribution parameters as structural terms and (smoothed) functions of independent variables. The proposed GEST model primarily addresses the difficulty in modelling time-varying skewness and kurtosis (beyond location and dispersion time series models). The originality of the thesis starts from Chapter 6 and in particular Chapter 7 and Chapter 8, with applications of the GEST model in Chapter 9. Chapters 2 and 3 contain the literature review of non-Gaussian time series models, Chapter 4 is a reproduction of Chapter 17 in Pawitan (2001), which contains an alternative method for estimating the hyperparameters instead of using the Kalman filter, and Chapter 5 is an application of Chapter 4 to smoothing Gaussian structural time series models.
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