ABSTRACT
But in many applications the values given for these quantities are quite unsafe, since no clear result of the numerical computation exists. The origin of this dilemma is twofold. On the one hand the assumption of low dimensionality may be wrong or inappropriate due to the existence of different length and time scales. Low in this sense means an attractor dimension of not more than about 5; otherwise, these quantities are hardly computable. But there is a second severe problem: all real data are contaminated with noise on small scales. All the above-mentioned quantities are defined in the limit of infinitely high resolution and generally the scaling behavior by which these quantities are defined sets in only on sufficiently small scales. Therefore, only if the noise level is small enough, the scaling behaviour can be seen. Thus one indispensable step in order to use these tools as a characterization of a system is to estimate the noise level and to do one’s best to reduce it. Of course, this is only one motivation for noise reduction. It is obvious that forecasting and model building can be improved by reducing the noise on the input data.
