Singular-spectrum analysis: a toolkit for short, noisy chaotic signals
Conference proceedings on Interpretation of time series from nonlinear mechanical systems
Rigorous computational shadowing of orbits of ordinary differential equations
Numerische Mathematik
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In the field of chaotic time series analysis, there is a lack of a distributional theory for the main quantities used to characterize the underlying data generating process (DGP). In this paper a method for resampling time series generated by a chaotic dynamical system is proposed. The basic idea is to develop an algorithm for building trajectories which lie on the same attractor of the true DGP, that is with the same dynamical and geometrical properties of the original data. We performed some numerical experiments on some short noise-free and high-noise series confirming that we are able to correctly reproduce the distribution of the largest finite-time Lyapunov exponent and of the correlation dimension.