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Sufficient conditions on state-space matrices A, C, G, R allow inferring them from a reduced-rank first-order vector autoregression (VAR) that can be computed with a Dynamic Mode Decomposition (DMD), thereby connecting DMD modes to hidden Markov states in the state-space system. When these sufficient conditions hold, our technique provides a fast way to infer parameters of the linear state space system. An application infers two macroeconomic aggregate factors from dynamics of CEX cross sections.

This paper provides an alternative computationally-efficient approach to approximate non- linear stochastic models. The novel method combines both perturbation and projection methods and draws on results from Koopman operator theory. I state convergence results and demonstrate its capabilities on a highly non-linear consumption- based asset-pricing model with external habits.