Precursors of extreme increments

Abstract

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.