S&P Dow Jones Indices LLC
Daily Index, Not Seasonally Adjusted
Daily, at close
The S&P 500 represents the stock market's performance by reporting the risks and returns of the biggest companies. It is used as the benchmark of the overall US stock market, to which all other investments are compared.
The data shows autocorrection and a non-normal distribution. The data should be differenced. While the Order Norm transformation, provides the best normality, the Yeo Johnson variable will also perform well.
Data is unable to be distributed by time or geography. The roll up method used is Weighted Average.
Auto Correction Function
Auto Correlation Function After Differencing
Partial Auto Correlation Function
Seasonal and Trend Decompostion
Data shows autocorrectation indicating a need for differencing
The ACF indicates 1 order differencing is appropriate.
Following first order differencing, no further differencing is required based on the differenced ACF at lag one of -0.50
The Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test, KPSS Trend = 2.96 p-value = 0.01 indicates that the data is not stationary.
The Shapiro-Wilk test returned W = 0.92 with a p-value =0.00 indicating the data does not follow a normal distribution.
A skewness score of -0.98 indicates the data are moderately skewed.
Hartigan's dip test score of 0.03 with a p-value of 0.00 inidcates the data is multimodal
Statistics (Pearson P/ df, lower => more normal)
S&P Dow Jones Indices LLC, S&P 500 [SP500], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/SP500, December 15, 2019.