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The effects of random forcing and deterministic feedback are combined in a measured multivariate time series. It is shown here how the characteristics of the driving noise can be found after the deterministic effects have been identified by the principal oscillation pattern (POP) analysis. In addition, the POP analysis is extended to enable the prediction of the most probable meteorological pattern at some future time when the present pattern is known, and the conditional probability of finding the process at any location within a range of values given the value of the process at another location at an earlier time. Estimates of how well these predictions can be trusted are also given. The basic assumption of POP analysis is that the system can be optimally modeled by a linear Markov process.
Cécile Penland (Sun,) studied this question.