Bayesian prediction for stochastic processes

Abstract

In many fields of statistical analysis, one is not only interested in estimation of model parameters, but in a prediction for future observations. For stochastic processes, on the one hand, one can be interested in the prediction for the further development of the current, i.e. observed, series. On the other hand, prediction for a new series can be of interest. This work presents two Bayesian prediction procedures based on the transition density of the Euler approximation, that include estimation uncertainty as well as the model variance. In a first algorithm, the pointwise predictive distribution is calculated, in a second, trajectories will be drawn. Both methods will be compared and analyzed with respect to their advantages and drawbacks and set in contrast to two commonly used prediction approaches.