On the Optimal Prediction of Extreme Events in Heavy‐Tailed Time Series With Applications to Solar Flare Forecasting

• DOI: 10.1111/jtsa.12820
• Publication Date: 2025-02-14T04:42:51Z
• Authors: Victor Verma; Stilian Stoev; Yang Chen
• Keywords: Solar flare; Flare

ABSTRACT The prediction of extreme events in time series is a fundamental problem arising many financial, scientific, engineering, and other applications. We begin by establishing general Neyman–Pearson‐type characterization optimal event predictors terms density ratios. This yields new insights several closed‐form for additive models. These results naturally extend to series, where we study both light‐ heavy‐tailed autoregressive moving average Using uniform law large numbers ergodic establish the asymptotic optimality an empirical version predictor multivariate regular variation, obtain expression extremal precision infinite averages, which provides theoretical bounds on ability predict extremes this class address important predicting solar flares applying our theory methodology state‐of‐the‐art consisting soft x‐ray flux measurements. Our demonstrate success limitations flare forecasting long‐memory models long‐range‐dependent, FARIMA