Berlin 2008 – wissenschaftliches Programm

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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme

AKSOE 16: Financial Markets and Risk Management III

AKSOE 16.1: Vortrag

Donnerstag, 28. Februar 2008, 13:30–14:00, EW 203

When are Extreme Events the easier to predict, the larger they are? — •S. Hallerberg and H. Kantz — Max-Planck-Institut für Physik komplexer Systeme, Dresden

We investigate the predictability of extreme events in time series. The focus of this work is to understand, under which circumstances large events are easier to predict than smaller events. Therefore we use a simple prediction algorithm based on precursory structures which are identified via conditional probabilities. Using the receiver operator characteristic curve as a measure for the quality of predictions we find that the dependence on the event size is closely linked to the probability distribution function of the underlying stochastic process. We evaluate this dependence on the probability distribution function analytically and numerically.

If we assume that the optimal precursory structures are used to make the predictions, we find that large increments are better predictable if the underlying stochastic process has a Gaussian probability distribution function, whereas larger increments are harder to predict, if the underlying probability distribution function has a power law tail. In the case of an exponential distribution function we find no significant dependence on the event size.

Furthermore we compare these results with predictions of increments in correlated data, i.e. , velocity increments of a free jet flow and wind speed measurements. The numerical results for predictions within free jet data comply well to the previous considerations for stochastical processes.