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Fast Bayesian updates for non-Gaussian dynamic linear models using quasi-sufficient statistics (Ridall, P.G. and Pettitt, A. N.)

West, Harrison and Wigan (1985) introduced a class of Bayesian dynamic generalised linear models where dynamic updates of the sufficient statistics were made by exploiting conjugacy. However the existence of sufficient statistics is rare in real world data. We extend the dynamic GLM methodology to models which do not have sufficient statistics but where proxys for them exist. These can be exploited to create closed form expressions for updates to the dynamic parameters and to the cumulative evidence for the model. We utilise fixed discount or forgetting parameters to down-weight observations from the more distant past. We illustrate this method with three applications. The first tracks the variation of the form of a basket-ball player over time The second tracks the form and style of premier league football teams over the last two decades. The third tracks the volatility of nine correlated stock-market returns over a period of time covering two major financial crashes.