Long memory behavior for simulated chaotic time series
Currently the long memory behavior is associated to stochastic processes. It can be modeled by different models such like the FARIMA processes, the k-factors GARMA processes or the fractal Brownian motion. On the other side, chaotic systems characterized by sensitivity to initial conditions and existence of an attractor are generally assumed to be close in their behavior to random white noise. Here we show why we can adjust a long memory process to well known chaotic systems defined in dimension one or in higher dimension. Using this new approach permits to characterize in another way the invariant measures associated to chaotic systems and to propose a way to make long term predictions: two properties which find applications in a lot of applied fields.
long memory behavior invariant measure predictions chaos deterministic systems stochastic systems