Abstract
One of the assumptions in the development of methods for identification and prediction of chaotic systems is that the time series is noise-free. The presence of noise limits the performance of many techniques of identification and prediction of chaotic systems [e.g., Schreiber and Kantz, 1996]. Since real data are inherently contaminated by noise, conclusions regarding the existence of chaos and hence the predictability in various physical and natural systems are often subject to debate. However, when the application of these methods to real data suggests the presence of a strong deterministic component, then naturally the next step is to look at the possibility of separating the deterministic signal from the noise toward improving the identification and prediction results. In their study, Porporato and Ridolfi [1997] provided clues to the existence of a strong deterministic component in the river flow data of Dora Baltea. Subsequently, they attempted to reduce the noise present in the data using a nonlinear noise reduction method [Schreiber and Grassberger, 1991] and reported improvements in the estimation of correlation dimension and prediction. The results are encouraging to hydrologists, who often have to deal with field data contaminated by noise. The purpose of the present discussion is to point out some of the potential problems in the application of such noise reduction methods to the river flow data (or any real data) and to highlight the existence of one possible approach to overcome these problems.