Estimation of noise levels for models of chaotic dynamical systems

We investigate how far it is possible to identify and separate dynamical noise from measurement noise in observed nonlinear time series. Using Bayesian methods, we derive estimates for the two noise levels, and find that, given a good model of the dynamics, these can give accurate results even if the dynamical noise level is orders of magnitude smaller than the measurement noise level, whereas a simple calculation of root mean square error badly understates the dynamical noise. We argue that this allows better estimates of the underlying dynamical time series, and so better predictions of its future and of its fundamental dynamical properties.