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Extreme event return times in long-term memory processes near 1/f

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Blender, R., Fraedrich, K. F., & Sienz, F. (2008). Extreme event return times in long-term memory processes near 1/f. Nonlinear Processes in Geophysics, 15(4), 557-565. doi:10.5194/npg-15-557-2008.

The distribution of extreme event return times and their correlations are analyzed in observed and simulated long-term memory (LTM) time series with 1/f power spectra. The analysis is based on tropical temperature and mixing ratio (specific humidity) time series from TOGA COARE with 1 min resolution and an approximate 1/f power spectrum. Extreme events are determined by PeakOver-Threshold (POT) crossing. The Weibull distribution represents a reasonable fit to the return time distributions while the power-law predicted by the stretched exponential for 1/f deviates considerably. For a comparison and an analysis of the return time predictability, a very long simulated time series with an approximate 1/f spectrum is produced by a fractionally differenced (FD) process. This simulated data confirms the Weibull distribution (a power law can be excluded). The return time sequences show distinctly weaker long-term correlations than the original time series (correlation exponent (gamma) over bar approximate to 0.56).