| Abstract: | We are interested in time series of the form y n =x n +ξ n where {x n } is generated by a chaotic dynamical system and where ξ n models observational noise. Using concentration inequalities, we derive fluctuation bounds for the auto-covariance function, the empirical measure, the kernel density estimator and the correlation dimension evaluated along y 0,…,y n , for all n. The chaotic systems we consider include for instance the Hénon attractor for Benedicks-Carleson parameters. |
