Estimating initial conditions for dynamical systems with incomplete information

J. Farmer, Blas Kolic and Juan Sabuco

INET Oxford Working Papers from Institute for New Economic Thinking at the Oxford Martin School, University of Oxford

Abstract: In this paper we study the problem of inferring the initial conditions of a dynamical system under incomplete information. Studying several model systems, we infer the latent microstates that best reproduce an observed time series when the observations are sparse, noisy and aggregated under a (possibly) nonlinear observation operator. This is done by minimizing the least-squares distance between the observed time series and a model-simulated time series using gradient-based methods. We validate this method for the Lorenz and Mackey-Glass systems by making out-of-sample predictions. Finally, we analyze the predicting power of our method as a function of the number of observations available. We find a critical transition for the MackeyGlass system, beyond which it can be initialized with arbitrary precision.

Pages: 17 pages
Date: 2021-09
New Economics Papers: this item is included in nep-ecm and nep-ore
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Persistent link: https://EconPapers.repec.org/RePEc:amz:wpaper:2021-20

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