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Beyond Location and Dispersion Models: The Generalized Structural Time Series Model with Applications

In many settings of empirical interest, time variation in the distribution parameters is important for capturing the dynamic behaviour of time series processes. Although the fitting of heavy tail distributions has become easier due to computational advances, the joint and explicit modelling of time-varying conditional skewness and kurtosis is a challenging task. We propose a class of parameter-driven time series models referred to as the generalized structural time series (GEST) model. The GEST model extends Gaussian structural time series models by a) allowing the distribution of the dependent variable to come from any parametric distribution, including highly skewed and kurtotic distributions (and mixed distributions) and b) expanding the systematic part of parameter-driven time series models to allow the joint and explicit modelling of all the distribution parameters as structural terms and (smoothed) functions of independent variables. The paper makes an applied contribution in the development of a fast local estimation algorithm for the evaluation of a penalised likelihood function to update the distribution parameters over time \textit{without} the need for evaluation of a high-dimensional integral based on simulation methods.