An approximate fast Bayesian algorithm for the analysis and forecasting of the lognormal time series

In this paper I consider a class of dynamic models with non-normal sampling distributions. An approximate algebraic propagation procedure to accommodate nonnormal dynamic processes is developed. This procedure, which is based upon the dynamic generalized linear models, can be applied to complex high-dimensional environments that change dynamically with time. The approximation is very fast and updating is achieved in closed form. An illustrative example of a process for predicting the spread of gaseous waste after an accident when the sampling distribution is lognormal is given.