# Dresden 2006 – wissenschaftliches Programm

## Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe

# DY: Dynamik und Statistische Physik

## DY 51: Non-Linear Stochastic Systems

### DY 51.3: Vortrag

### Freitag, 31. März 2006, 12:00–12:15, H\"UL 186

**Precursors of Extreme Increments** — •Sarah Hallerberg, Eduardo G. Altmann, Detlef Holstein, and Holger Kantz — Max Planck Institute for the Physics of Complex Systems

Noethnitzer Str. 38,

We investigate precursors and predictability of extreme events in time series, which consist in large increments within successive time steps. We determine analytically the marginal and the joint probability density function (PDF) for large increments in uncorrelated random numbers and AR(1)- correlated data. These PDFs provide us with different possibilities to choose convenient precursors for the events we are looking for. The performance of these precursors is then tested via creating receiver operator characteristics (ROC). Surprisingly we obtain better predictions for completely uncorrelated Gaussian random numbers than for AR(1)- correlated data. This apparent paradox can be qualitatively explained by clustering of the AR(1)- correlated data, which inhibits large increments. Additionally we present a quantitative discussion of this effect by using a not common summary index for smooth ROC- curves. Furthermore this index can be used to estimate the quality of smooth ROC- curves for any given event size and correlation strength.