标题： 高频金融收益的重复间隔分析及其在风险估计中的应用 显示英文标题

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

摘要： 我们研究了两个指数和中国股市中20只个股在正阈值$q>0$以上或负阈值$q<0$以下的连续1分钟收益率之间的复发间隔$\tau$的概率分布。 正阈值和负阈值的复发间隔分布是对称的，并通过三种拟合优度测量方法测试了幂律尾部，包括Kolmogorov-Smirnov (KS) 统计量、加权KS统计量和Cramér-von Mises准则。 在正阈值和负阈值的复发间隔中观察到了长期和短期记忆效应$q$。 我们进一步将复发间隔分析应用于基于概率$W_q(\Delta{t},t)$、风险价值（VaR）分析以及基于前序复发间隔的VaR分析的中国股市风险估计。 显示英文摘要

摘要： We investigate the probability distributions of the recurrence intervals $\tau$ 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 Cram\'er-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 $W_q(\Delta{t},t)$, Value-at-Risk (VaR) analysis and VaR analysis conditioned on preceding recurrence intervals.