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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
1987 Great Storm: Terrible blow, not a knockout, Daily Telegraph, 13 October 2007.
Great Storm of 1987, English wikipedia, http://en.wikipedia.org/wiki/Great_Storm_of_1987
Starkniederschläge in Sachsen im August 2002, Publication of the German Weather Service DWD October 2002
User Guide to ECMWF Forecast Products, http://www.ecmwf.com/products/forecasts/guide/index.html
G. E. P. Box, G. M. Jenkins, G. C. Reinsel, Time Series Analysis, Prentice-Hall Inc. (1994)
P. J. Brockwell, R. A. Davis, Time Series: Theory and Methods, Springer (1998)
H. Kantz, M. Ragwitz, Phase space reconstruction and nonlinear predictions for stationary and nonstationary Markovian processes, Int. J. Bifurcation Chaos, 14 1935–1945 (2004)
D. J. Jackson, Hypothesis testing and earthquake prediction, Proc. Natl. Acad. Sci. USA, 93, 3772–3775 (1996)
C. E. Elger, K. Lehnertz, Seizure prediction by non-linear time series analysis of brain electrical activity, Eur. J. Neurosci., 10, 786–789 (1998)
I. J. Good, Rational decisions, J. Royal Statist. Soc., XIV(1) B, 107–114 (1952)
Jr. J. L. Kelly, A new interpretation of information rate, Bell System Techn. J., 35, 917–926 (1956)
T. A. Brown, Probabilistic Forecasts and Reproducing Scoring Systems, RAND Corporation RM–6299–ARPA (1970)
L. J. Savage, Elicitation of personal probabilities and expectation, J. Amer. Statist. Ass., 66, 783–801 (1971)
J. Bröcker, L. A. Smith, Scoring probabilistic forecasts: the importance of being proper, Weather and Forecasting, 22, 382–388 (2007)
J. P. Egan, Signal Detection Theory and ROC Analysis, Academic Press (1975)
A. M. Mood, F. A. Graybill, D. C. Boes, Introduction to the Theory of Statistics, McGraw-Hill (1974)
S. Hallerberg, E. G. Altmann, D. Holstein, H. Kantz, Precursors of extreme increments, Phys. Rev. E, 75, 016706 (2007)
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)
S. Hallerberg, H. Kantz, Influence of the event magnitude on the predictability of extreme events, Phys. Rev. E, 77, 011108 (2008)
A. B. Shapoval, M. G. Shrirman, How size of target avalanches influence prediction efficiency, Int. J. Mod. Phys. C, 17 1777–1790 (2006)
D. Lamper, S. D. Howison, N. F. Johnson, Predictability of large future changes in a competitive evolving population, Phys. Rev. Lett., 88, 017902 (2002)
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
C. Renner, J. Peinke, R. Friedrich, Experimental indications for Markov properties of small-scale turbulence, J. Fluid. Mech., 433 383–409 (2001)
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)
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)
U. Frisch, Turbulence, Cambridge University Press, Cambridge (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-540-78938-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78937-6
Online ISBN: 978-3-540-78938-3
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)