Interval forecasting using artificial neural networks trained with Monte Carlo Markov Chain methods

Recent work showed that Bayesian formulation of the neural networks' training problem provide a

natural way to account for the uncertainty associated with the resulting predictions.

This study employs Markov Chain Monte Carlo methods, which make possible feasible

implementations within the Bayesian framework, to produce a conditional predictive distribution in

time series forecasting. [t exploits the advantages of the 'mean absolute deviations' error function (as

opposed to the 'mean squared error' used in backpropagation) to address the non-trivial cases where

uniformity of the prediction error bounds over the state space or where the assumption of normally

distributed error terms do not hold. The conditional quantiles of the predicted variable are then natural

estimators of the 'prediction intervals' associated with a prespecified probability level. The length of

these intervals is subsequently used to monitor the evolution of the prediction uncertainty over the

state space as well as in m-step ahead predictions.

To illustrate the properties of our estimators we discuss results in the following cases: (a) an AR( 1 )

model with Gaussian and non-Gaussian disturbances, (b) the logistic map (chaotic) with added

Gaussian noise, and finally, (c) a real-world financial time series.