Estimation of intensive quantities in spatio-temporal systems from time-series

We study multivariate time-series generated by coupled map lattices exhibiting spatio-temporal chaos and investigate to what extent we are able to estimate various intensive measures of the underlying system without explicit knowledge of the system dynamics. Using the rescaling and interleaving properties of the Lyapunov spectrum of systems in a spatio-temporally chaotic regime and paying careful attention to errors introduced by sub-system boundary effects, we develop algorithms that are capable of estimating the Lyapunov spectrum from time-series. We analyse the performance of these and find that the choice of basis used to fit the dynamics is crucial: when the local dynamics at a lattice site is well approximated by this basis we are able to accurately determine the full Lyapunov spectrum. However, as the local dynamics moves away from the space spanned by this basis, the performance of our algorithm deteriorates.