  We investigate precursors and predictability of extreme increments in a time
series. The events we are focusing on consist in large increments within
successive time steps. We are especially interested in understanding how the
quality of the predictions depends on the strategy to choose precursors, on the
size of the event and on the correlation strength. We study the prediction of
extreme increments analytically in an AR(1) process, and numerically in wind
speed recordings and long-range correlated ARMA data. We evaluate the success
of predictions via receiver operator characteristics (ROC-curves). Furthermore,
we observe an increase of the quality of predictions with increasing event size
and with decreasing correlation in all examples. Both effects can be understood
by using the likelihood ratio as a summary index for smooth ROC-curves.
