Optimal state space reconstruction via Monte Carlo decision tree search

Abstract A novel idea for an optimal time delay state space reconstruction from uni- and multivariate series is presented. The entire embedding process considered as a game, in which each move corresponds to cycle subject evaluation through objective function. This way the procedure can be modeled tree, leaf holds specific value of By using Monte Carlo ansatz, proposed algorithm populates tree with many leafs by computing different possible paths final chosen that particular path, ends at lowest achieved method aims prevent getting stuck local minimum function used modular way, enabling practitioners choose statistic delays well suitable themselves. guarantees optimization over parameter long sampled sufficiently. As proof concept, we demonstrate superiority classical methods variety application examples. We compare recurrence plot-based statistics inferred reconstructions Lorenz-96 system highlight improved forecast accuracy map-like model data palaeoclimate isotope series. Finally, utilize detection causality its strength between observables gas turbine type thermoacoustic combustor.