Kolmogorov-Smirnov simultaneous confidence bands for time series distribution function
Kolmogorov-Smirnov simultaneous confidence bands for time series distribution function
复制标题
时间序列分布函数的柯尔莫哥洛夫-斯米尔诺夫同时置信带
DOI：
10.1007/s00180-021-01149-5
复制
发表时间：
2021-09-18
影响因子：
1.3
通讯作者：
Yang, Lijian
中科院分区：
文献类型：
--
作者：
Li, Jie;Wang, Jiangyan;Yang, Lijian
由于缺乏检验假设的工具，关于时间序列分布的断言往往是未经证实的断言，而不是经过证实的结论。在这项工作中，Kolmogorov-Smirnov型同步置信带（SCBs）是基于从时间序列实现中提取的简单随机样本（sss）构建的，并使用核分布估计器（KDE）代替SRS的经验累积分布函数构建平滑SCBs。所有SCBs都具有与标准Kolmogorov-Smirnov相同的极限分布，这在各种时间序列上的模拟实验中得到了验证。对标准化的标准普尔500日收益数据计算这些scb会得到一些意想不到的发现，即自由度不小于3的学生t分布和正态分布都是标准化日收益序列分布的可接受版本，经过适当的重新缩放。这些发现对长期以来认为每日金融回报分布是厚尾和细峰分布的观点提出了挑战。
Claims about distributions of time series are often unproven assertions instead of substantiated conclusions for lack of hypotheses testing tools. In this work, Kolmogorov-Smirnov type simultaneous confidence bands (SCBs) are constructed based on simple random samples (SRSs) drawn from realizations of time series, together with smooth SCBs using kernel distribution estimator (KDE) instead of empirical cumulative distribution function of the SRS. All SCBs are shown to enjoy the same limiting distribution as the standard Kolmogorov-Smirnov for i.i.d. sample, which is validated in simulation experiments on various time series. Computing these SCBs for the standardized S&P 500 daily returns data leads to some rather unexpected findings, i.e., student's t-distributions with degrees of freedom no less than 3 and the normal distribution are all acceptable versions of the standardized daily returns series' distribution, with proper rescaling. These findings present challenges to the long held belief that daily financial returns distribution is fat-tailed and leptokurtic.