Many noisy data in our daily life are not independent but exhibit short or long range correlations. The different kinds of correlations can considerably inuence the structure of a record and thus need to be considered in data analysis, in particular in the analysis of climate records that are known to exhibit long-range correlations.
Random (noisy) processes can be characterized by the way consecutive data are correlated. The data can be uncorrelated (white noise), short-range correlated (often called red noise), or long-range correlated (sometimes called pink noise). Here we describe the properties and applications of these different kinds of noise. We discuss, how they influence (i) the diffusion process, (ii) the occurrence of rare extreme events and (iii) the detection of an external trend that is superimposed on the noise; (ii) and (iii) are particularly relevant in the context of detecting anthropogenic global warming by data analysis.Zum Volltext