Filtering and Prediction in Noncausal Processes

This paper revisits the filtering and prediction in noncausal and mixed autoregressive processes and provides a simple alternative set of methods that are valid for processes with infinite variances. The prediction method provides complete predictive densities and prediction intervals at any finite horizon H, for univariate and multivariate processes. It is based on an unobserved component representation of noncausal processes. The filtering procedure for the unobserved components is provided along with a simple back-forecasting estimator for the parameters of noncausal and mixed models and a simulation algorithm for noncausal and mixed autoregressive processes. The approach is illustrated by simulations