Recurrence interval analysis of high-frequency financial returns and its application to risk estimation

Abstract

We investigate the probability distributions of the recurrence intervals τ between consecutive 1-min returns above a positive threshold q>0 or below a negative threshold q<0 of two indices and 20 individual stocks in China's stock market. The distributions of recurrence intervals for positive and negative thresholds are symmetric, and display power-law tails tested by three goodness-of-fit measures, including the Kolmogorov–Smirnov (KS) statistic, the weighted KS statistic and the Cramér–von Mises criterion. Both long-term and shot-term memory effects are observed in the recurrence intervals for positive and negative thresholds q. We further apply the recurrence interval analysis to the risk estimation for the Chinese stock markets based on the probability Wq(Δt,t), value-at-risk (VaR) analysis and VaR analysis conditioned on preceding recurrence intervals.