Piecewise Solutions to Big Data

Outliers in the financial market data often carry important information, which requires attention and investigation. Many outlier detection techniques, including both parametric and nonparametric, have been developed over the years which are specific to certain application domains. Nonetheless, outlier detection is not an easy task, because sometimes the occurrence of them is pretty easy and evident, but in some other times, it may be extremely cumbersome. Financial series, which are not only pretty sensitive in reflecting the world market conditions due to the interactions of a very large number of participants in its operation, but also influenced by other stock markets that operate in other parts of the world, produce a non-synchronous process. In this research, we detect the presence of outliers in financial time series over the S&P 500 during the year 2016. We detect the beginning of some shocks (outliers) such as the Brexit referendum and the United States Presidential election held in the year 2016. Generally, the impacts of these events were not drastic. Histogram time series was implemented over a daily closing price on intervals of five minutes for the S&P 500 index during 2015 and 2016. In this case, the linear dependency between days of atypical returns were analyzed on quantiles [0 ?? 40]% and [60 ?? 100]%, while Wassertein distance and an approximation of entropy were used to quantify the presence of instant shocks in the index.