Extracting low-order stochastic models from data

We present a numerical technique to derive optimal stochastic models (Markov chains or SDEs) for the description of the evolution of a few interesting variables in large-sized dynamical systems. The technique is based on constructing the stochastic model whose eigenfunctions and eigenvalues are the closest, in some appropriate norm, to the ones gathered from (possibly non-Markovian) timeseries. We apply the technique by extracting a stochastic model for the temporal evolution of the first few principal components taken from an atmosphere model dataset.