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Part of the book series: Lecture Notes in Earth Sciences ((LNEARTH,volume 112))

Abstract

We discuss concepts for the prediction of extreme events based on time series data. We consider both probabilistic forecasts and predictions by precursors. Probabilistic forecasts employ estimates of the probability for the event to follow, whereas precursors are temporal patterns in the data typically preceeding events. Theoretical considerations lead to the construction of schemes that are optimal with respect to several scoring rules. We discuss scenarios for which, in contrast to intuition, events with larger magnitude are better predictable than events with smaller magnitude.

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References

  1. 1987 Great Storm: Terrible blow, not a knockout, Daily Telegraph, 13 October 2007.

    Google Scholar 

  2. Great Storm of 1987, English wikipedia, http://en.wikipedia.org/wiki/Great_Storm_of_1987

    Google Scholar 

  3. Starkniederschläge in Sachsen im August 2002, Publication of the German Weather Service DWD October 2002

    Google Scholar 

  4. User Guide to ECMWF Forecast Products, http://www.ecmwf.com/products/forecasts/guide/index.html

    Google Scholar 

  5. G. E. P. Box, G. M. Jenkins, G. C. Reinsel, Time Series Analysis, Prentice-Hall Inc. (1994)

    Google Scholar 

  6. P. J. Brockwell, R. A. Davis, Time Series: Theory and Methods, Springer (1998)

    Google Scholar 

  7. H. Kantz, M. Ragwitz, Phase space reconstruction and nonlinear predictions for stationary and nonstationary Markovian processes, Int. J. Bifurcation Chaos, 14 1935–1945 (2004)

    Article  Google Scholar 

  8. D. J. Jackson, Hypothesis testing and earthquake prediction, Proc. Natl. Acad. Sci. USA, 93, 3772–3775 (1996)

    Article  Google Scholar 

  9. C. E. Elger, K. Lehnertz, Seizure prediction by non-linear time series analysis of brain electrical activity, Eur. J. Neurosci., 10, 786–789 (1998)

    Article  Google Scholar 

  10. I. J. Good, Rational decisions, J. Royal Statist. Soc., XIV(1) B, 107–114 (1952)

    Google Scholar 

  11. Jr. J. L. Kelly, A new interpretation of information rate, Bell System Techn. J., 35, 917–926 (1956)

    Google Scholar 

  12. T. A. Brown, Probabilistic Forecasts and Reproducing Scoring Systems, RAND Corporation RM–6299–ARPA (1970)

    Google Scholar 

  13. L. J. Savage, Elicitation of personal probabilities and expectation, J. Amer. Statist. Ass., 66, 783–801 (1971)

    Article  Google Scholar 

  14. J. Bröcker, L. A. Smith, Scoring probabilistic forecasts: the importance of being proper, Weather and Forecasting, 22, 382–388 (2007)

    Article  Google Scholar 

  15. J. P. Egan, Signal Detection Theory and ROC Analysis, Academic Press (1975)

    Google Scholar 

  16. A. M. Mood, F. A. Graybill, D. C. Boes, Introduction to the Theory of Statistics, McGraw-Hill (1974)

    Google Scholar 

  17. S. Hallerberg, E. G. Altmann, D. Holstein, H. Kantz, Precursors of extreme increments, Phys. Rev. E, 75, 016706 (2007)

    Article  Google Scholar 

  18. S. Hallerberg, H. Kantz, How does the quality of a prediction depend on the magnitude of the events under study?, Nonlin. Proc. Geophys., 15, 321–331 (2008)

    Article  Google Scholar 

  19. S. Hallerberg, H. Kantz, Influence of the event magnitude on the predictability of extreme events, Phys. Rev. E, 77, 011108 (2008)

    Article  Google Scholar 

  20. A. B. Shapoval, M. G. Shrirman, How size of target avalanches influence prediction efficiency, Int. J. Mod. Phys. C, 17 1777–1790 (2006)

    Article  Google Scholar 

  21. D. Lamper, S. D. Howison, N. F. Johnson, Predictability of large future changes in a competitive evolving population, Phys. Rev. Lett., 88, 017902 (2002)

    Article  Google Scholar 

  22. The wind-speed data were recorded at the Riso National Laboratory, Technical University of Denmark, http://www.risoe.dk/vea, see also http://winddata.com

    Google Scholar 

  23. C. Renner, J. Peinke, R. Friedrich, Experimental indications for Markov properties of small-scale turbulence, J. Fluid. Mech., 433 383–409 (2001)

    Google Scholar 

  24. C. W. Van Atta, J. Park, Statistical self-similarity and initial subrange turbulence, In: Statistical Models and Turbulence, Lect. Notes in Phys. 12, pp 402–426, eds. M. Rosenblatt and C. W. Van Atta, Springer Berlin (1972)

    Google Scholar 

  25. Y. Gagne, E. Hopfinger, U. Frisch, A new universal scaling for fully developed turbulence: the distribution of velocity increments. In: New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena, NATO ASI 237, pp 315–319, eds. P. Coullet and P. Huerre, Plenum Press, New York (1990)

    Google Scholar 

  26. U. Frisch, Turbulence, Cambridge University Press, Cambridge (1995)

    Google Scholar 

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Hallerberg, S., Bröcker, J., Kantz, H. (2008). Prediction of Extreme Events. In: Donner, R.V., Barbosa, S.M. (eds) Nonlinear Time Series Analysis in the Geosciences. Lecture Notes in Earth Sciences, vol 112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78938-3_3

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