Linear Inverse Modeling (LIM) has been used by many researchers for prediction and diagnosis of geophysical processes such as El Nino and low frequency atmospheric variability. The underlying assumption of this technique is that the dynamics represented in a multivariate time series can be well approximated as a linear Markov process driven by additive white noise.

We present a generalization of LIM. In "Multiplicative LIM", the strength of the stochastic forcing may be proportional to the state of the system itself. Further, we allow the presence of deterministic external forcing in the dynamical description. These modifications to LIM allow for more realistic empirical models of geophysical systems than has been possible in previous studies.