Interval forecasting using artificial neural networks trained with Monte Carlo Markov Chain methods
Konstantinos Sirlantzis · Kent Academic Repository (University of Kent) · 1998
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.