Identification of Symmetric Noncausal Processes: Cross-Directional Response Modelling of Paper Machines

We adapt the maximum likelihood method to treat symmetric noncausal models. Such models govern the cross-directional response of paper machines: they are noncausal in space, not in time. Process symmetry is essential to our methods. We show that every symmetric noncausal process admits a spectrally equivalent causal model, then prove that the maximum likelihood estimate of this causal model converges to that of the original noncausal process. A numerical example illustrates the method