Adapting extreme value statistics to financial time series: dealing with bias and serial dependence
研究了在金融时间序列存在弱序列依赖时，如何联合处理极值分析中的偏差和序列依赖问题，提出了极值指数和高分位数的渐近无偏估计量，并应用于道琼斯工业平均指数日收益率的在险价值估计。
We handle two major issues in applying extreme value analysis to financial time series, bias and serial dependence, jointly. This is achieved by studying bias correction methods when observations exhibit weak serial dependence, in the sense that they come from ?-mixing series. For estimating the extreme value index, we propose an asymptotically unbiased estimator and prove its asymptotic normality under the ?-mixing condition. The bias correction procedure and the dependence structure have a joint impact on the asymptotic variance of the estimator. Then we construct an asymptotically unbiased estimator of high quantiles. We apply the new method to estimate the value-at-risk of the daily return on the Dow Jones Industrial Average index.