BSR Forecasting by partial simulation

[Víctor de Buen Remiro]

Bayesian forecasting is only an special case of bayesian simulation where the unknown parameters are just future values of observational nodes that can be treated as missing values.

From the original BSR model it's posible to isolate these missing values in a new BSR model which target is to give a mechanism of arbitrary inference over future values.

Partial simulation is the simplest and fastest way to implement bayesian forecasting from an old stored MCMC by means of a modified version of estimation model. It consists in an automated and easy to use way of selecting which variables must be fixed or reloaded from chains simulated in past estimation sessions.

Fixing variables to the estimated average is the faster way but it means to calculate forecasting conditioned by just one realization of parameters. It's a bayesian way but not too.

Reloading past MCMC is more robust for inference, specially when there are no enough data, or estimated parameters are no strongly significative. Since future missing values cannot have influence over past, if there are no new data, the parameters obtained in the final estimate are as good as the day they were estimated. If there are new data, then it could be needed a battery of diagnostic tests in order to ensure the quality of the model.

These are the steps to convert the original estimation model in a bayesian forecasting model:

• Select a past model session, whose MCMC has been stored in a persistent device.
• Mark as fixed or reloaded all well known variables available
• Select a short contrast time window, according with the ARIMA degrees, in order to get faster simulations.
• Add missing output variables along forecasts window time.
• Add known input values along forecasts window time.
• Add posible missing input variables along forecasts window time
• Add strong prior information over missing output and input variables to avoid colinearity.
• Finally it's no problem to add some new detected variables in just one step of reestimation and forecasting.