S&P 500

Source:
S&P Dow Jones Indices LLC

Release:
S&P

Units:
Daily Index, Not Seasonally Adjusted

Frequency:
Daily, at close

Available Through:
12/06/2021

Why Use:

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.

Suggested Treatment:

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.

Grain Transformation:

Data is unable to be distributed by time or geography. The roll up method used is Weighted Average.

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S&P 500

Auto Correction Function

Auto Correlation Function After Differencing

Partial Auto Correlation Function

Seasonal Impact

Seasonal and Trend Decompostion

Autocorrectation Analysis:

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

Trend Analysis:

The Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test, KPSS Trend = 2.96 p-value = 0.01 indicates that the data is not stationary.

Distribution Analysis:

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)

No transform
5.54
Box-cox
NA
Log_b(x-a)
NA
sqrt(x+a)
10.02
exp(x)
NA
arcsinh(x)
45.60
Yeo-Johnson
5.32
OrderNorm
1.13

Citation:

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.

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