This article discusses filtering, prediction and simulation in univariate and multivariate noncausal processes. A closed-form functional estimator of the predictive density for noncausal and mixed processes is introduced that provides prediction intervals up to a finite horizon H. A state-space representation of a noncausal and mixed multivariate vector autoregressive process is derived in two ways-by the partial fraction decomposition or from the real Jordan canonical form. A recursive BHHH algorithm for the maximization of the approximate log-likelihood function is proposed, which calculates the filtered values of the unobserved causal and noncausal components of the process. The new methods are illustrated by a simulation study involving a univariate noncausal process with infinite variance.