• chaotic
• denoising
• dynamical systems
• logistic map
• statistical inference
• time series

In this thesis we consider the problem of statistical inference for discrete dynamical systems with a special concern on the difficulties that arise in presence of chaotic dynamics. We analyze different algorithms found in the literature for the estimation of parameter of these systems, and the denoising of time series of observations, affected by random errors, of their orbits. We try to assess the performance of these procedures with numerical simulation methods and, when they are possible, with theoretical considerations. We also propose a modification to one of the considered algorithm that try to improve its performance in the chaotic regime.
At last, we propose a theoretical criterion that assesses the possibility of denoising for some discrete dynamical systems, depending on the metric entropy of the set of all orbits up to a certain number of iterations of the map that define the dynamics.