本福德定律对S& P500日收盘价和相应的日对数收益率的检验都表明存在巨大的不一致性
Benford's laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity
摘要：
所谓的本福德定律经常被用来观察数据集中的异常和异常，特别是选举结果和财务报表。然而，基本的金融市场指数没有得到太多的研究，如果研究，在这样的角度。本文介绍了S\&P500日收盘值的分布特征和相应的日日志回报在一个很长的时间间隔，[03/01/1950 - 22/08/2014]，共计16265个数据点。我们解决的第一，第二，和前两个有效数字计数的频率，并探讨符合本福德的法律，这些分布在五个不同的（相等的大小）水平的分解。研究了正或负情况下的对数收益。标准普尔500指数每日收盘价的结果显示，无论不同的分解水平如何，都存在巨大的不一致性。一些“第一位数”和“前两位数”值甚至缺失。这种不一致的原因进行了讨论，指出在巨大的数据库，从而得出“明确的结论”，把本福德的法律是理所当然的危险。与本福德定律的协议是更好的日志返回。这种一致性的差异可以在数据集本身中找到解释：指数的内在趋势。为了进一步验证这一点，每日回报率进行了模拟校准模拟与观察到的数据平均值和测试对本福德的法律。人们发现，不仅趋势，而且分布的标准差是相关参数，在结论符合本福德定律。
英文摘要：
The so-called Benford's laws are of frequent use in order to observe anomalies and regularities in data sets, in particular, in election results and financial statements. Yet, basic financial market indices have not been much studied, if studied at all, within such a perspective. This paper presents features in the distributions of S\&P500 daily closing values and the corresponding daily log returns over a long time interval, [03/01/1950 - 22/08/2014], amounting to 16265 data points. We address the frequencies of the first, second, and first two significant digits counts and explore the conformance to Benford's laws of these distributions at five different (equal size) levels of disaggregation. The log returns are studied for either positive or negative cases. The results for the S&P500 daily closing values are showing a huge lack of non-conformity, whatever the different levels of disaggregation. Some "first digits" and "first two digits" values are even missing. The causes of this non-conformity are discussed, pointing to the danger in taking Benford's laws for granted in huge databases, whence drawing "definite conclusions". The agreements with Benford's laws are much better for the log returns. Such a disparity in agreements finds an explanation in the data set itself: the inherent trend in the index. To further validate this, daily returns have been simulated calibrating the simulations with the observed data averages and tested against Benford's laws. One finds that not only the trend but also the standard deviation of the distributions are relevant parameters in concluding about conformity with Benford's laws.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
