Fernandes, Cristiano Augusto Coelho
(1991)
Non-Gaussian structural time series models.
PhD thesis, London School of Economics and Political Science.
Abstract
This thesis aims to develop a class of state space models for non-Gaussian time series. Our models are based on distributions of the exponential family, such as the Poisson, the negative-binomial, the binomial and the gamma. In these distributions the mean is allowed to change over time through a mechanism which mimics a random walk. By adopting a closed sampling analysis we are able to derive finite dimensional filters, similar to the Kalman filter. These are then used to construct the likelihood function and to make forecasts of future observations. In fact for all the specifications here considered we have been able to show that the predictions give rise to schemes based on an exponentially weighted moving average (EWMA). The models may be extended to include explanatory variables via the kind of link functions that appear in GLIM models. This enables nonstochastic slope and seasonal components to be included. The Poisson, negative binomial and bivariate Poisson models are illustrated by considering applications to real data. Monte Carlo experiments are also conducted in order to investigate properties of maximum likelihood estimators and power studies of a post sample predictive test developed for the Poisson model.
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