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 in 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 . Maximizing the usefulness of extreme forecasts to define an optimized hazard threshold, we indicate 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.

Keywords:

• Extreme return
• Risk estimation
• Recurrence interval
• Return forecasting
• Hazard probability

AMS Subject Classifications:

• G130
• G110

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Z.-Q.J. and W.-X.Z. acknowledge support from the National Natural Science Foundation of China (71131007 and 71532009), China Scholarship Council (201406745014) and the Fundamental Research Funds for the Central Universities (222201718006). G.-J.W. and C.X. acknowledge support from the National Natural Science Foundation of China (71501066, 71373072, and 71521061). A.C. acknowledges the support from Brazilian agencies FAPEAL (PPP 20110902-011-0025-0069/60030-733/2011) and CNPq (PDE 20736012014-6, Universal 423713/2016-7). H.E.S. was supported by NSF (Grants CMMI 1125290, PHY 1505000, and CHE- 1213217) and by DOE Contract (DE-AC07-05Id14517).