Seminarium Fizyki Materii Skondensowanej

In this talk, I will review our recent results on the statistics of return intervals between events above some threshold Q (a) in long-termcorrelated (monofractal) records where the linear autocorrelation function decreases by a power law and (b) in multifractal data sets where the linear autocorrelation function vanishes and only non-linear correlations are present. Both monofractal and multifractal data sets play an important role in geoscience, examples are temperature records, river flows, and precipitation, as well as in the financial markets, in physiology and in internet traffic. It is shown how the long-term memory affects the statistics of the return intervals. For monofractal data, the memory leads to a stretched exponential decay of the probability density function (pdf) and to long-term correlations between the return intervals, which then in turn leads to a clustering of extreme events. These characteristic features can be seen in long natural and reconstructed climate records. In multifractal data sets, the non-linear memory leads to pronounced long-term correlations of the return intervals and to a pdf that decays by a power law, a fact that can be used.