Short term prediction of extreme returns based on the recurrence interval analysis

Abstract: Being able to predict the occurrence of extreme returns is important in financial risk management. Using the distribution of recurrence intervals---the waiting time between consecutive extremes---we show that these extreme returns are predictable on the short term. Examining a range of different types of returns and thresholds we find that recurrence intervals follow a $q$-exponential distribution, which we then use to theoretically derive the hazard probability $W(\Delta t |t)$. Maximizing the usefulness of extreme forecasts to define an optimized hazard threshold, we indicates a financial extreme occurring within the next day when the hazard probability is greater than the optimized threshold. Both in-sample tests and out-of-sample predictions indicate that these forecasts are more accurate than a benchmark that ignores the predictive signals. This recurrence interval finding deepens our understanding of reoccurring extreme returns and can be applied to forecast extremes in risk management.