Aspects of forecasting aggregate and discrete data
This work studies three related topics arising from the problem of forecasting airline passenger bookings. The first topic concerns the initialization through the starting prior for a DLM (Dynamic Linear Model) or Generalized DLM. An approach is given which uses the first observations of the series much more efficiently than that suggested by Pole and West. Proper marginal priors are derived for stationary model components and proper marginal priors may be obtained for parameter subspaces and used for forecasting within that subspace well before a full proper prior is available. The second topic proposes a model to forecast the number of people booking tickets for particular flights. The model is more realistic than those which are classically used, since it is a dynamic model and acknowledges discrete distributions. The basic idea is given by the Dynamic Generalized Linear Model and a key feature is given by the gamma to log-normal approximation that is developed. The third topic consists of a study of temporal aggregation of a process that can be represented by a DLM. We give representation results for the simplest univariate cases, reveal some surprising phenomena, such as drastic model simplification with aggregation, and discuss some advantages and disadvantages of using the aggregated observations, depending on the forecasting objectives, as well as the importance of aggregation in our particular booking problem.