Effect of noise filtering on predictions: on the routes of chaos

The detection of chaotic behaviors in commodities, stock markets and weather data is usually complicated by large noise perturbation inherent to the underlying system. It is well known, that predictions, from pure deterministic chaotic systems can be accurate mainly in the short term. Thus, it will be important to be able to reconstruct in a robust way the attractor in which evolves the data, if this attractor exists. In chaotic theory, the deconvolution methods have been largely studied and there exist different approaches which are competitive and complementary. In this work, we apply two methods : the singular value method and the wavelet approach. This last one has not been investigated a lot of filtering chaotic systems. Using very large Monte Carlo simulations, we show the ability of this last deconvolution method. Then, we use the de-noised data set to do forecast, and we discuss deeply the possibility to do long term forecasts with chaotic systems.