Filtering, Prediction and Simulation Methods for Noncausal Processes

Abstract

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.