On the predictability of extreme events in records with linear and nonlinear long-range memory: Efficiency and noise robustness

We study the predictability of extreme events in records with linear and nonlinear long-range memory in the presence of additive white noise using two different approaches: (i) the precursory pattern recognition technique (PRT) that exploits solely the information about short-term precursors, and (ii) the return interval approach (RIA) that exploits long-range memory incorporated in the elapsed time after the last extreme event. We find that the PRT always performs better when only linear memory is present. In the presence of nonlinear memory, both methods demonstrate comparable efficiency in the absence of white noise. When additional white noise is present in the record (which is the case in most observational records), the efficiency of the PRT decreases monotonously with increasing noise level. In contrast, the RIA shows an abrupt transition between a phase of low level noise where the prediction is as good as in the absence of noise, and a phase of high level noise where the prediction becomes poor. In the phase of low and intermediate noise the RIA predicts considerably better than the PRT, which explains our recent findings in physiological and financial records.