This code is the how the results from the thesis "An Analysis of Financial Markets via Benford's Law" were achieved.
The two data thats needed to run is one stocks "csv" file from yahoo finance that contains the date interval for the rest of the data adjusting the code to function for other date inputs shouldn't be difficult though. The second is the Prices((CP) Closing Prices used) matrix you want to analyse, I included the datasets so you know what they should look like.
The data I provided should be input like so;
- AAPLold.csv with CPS_240_617_1994
- AAPL.csv with CPS_361_617_2007 (Data used to replicate the paper (1))
- TSLA.csv with CPS_449_617_2020 (Small note the this CPS is different than that in thesis)
A small run down of the code goes,
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data colleting first.
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adjusting prices and then using the function "benford_extract" by (2) to find the distributions of both prices and log returns.
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A plot of the distribution against uniform and benfords expected distibution for comparison.
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Chi-square goodness of fit test on the data against benford and uniform.
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Using benford_extract again to find the day-by-day distributions.
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Finding the amount of days that accept the two null hypotheseses and sorting the rejected days to see how many days where consecutively rejected.
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Finally plotting the most and least accepted day and showing in a scatterplot all days and how they accept or reject the null.
The data is expected to reject the null this is due to the large sample as the chi-square goodness-of-fit test exponentiates tiny differences between the two datasets being compared the important result from this test is the level of conformity to benford is far greater than that to the uniform distribution which is why we say the data follows Benford's Law.
References:
(1) Marco Corazza, Andrea Ellero, and Alberto Zorzi. Checking financial markets via ben-ford’s law: the s&p 500 case. In Marco Corazza and Claudio Pizzi, editors, Mathematicaland Statistical Methods for Actuarial Sciences and Finance, pages 93–102, Milano, 2010.Springer Milan
(2) Tommaso Belluzzo. Benford’s law. https://github.com/TommasoBelluzzo/BenfordLaw, (2021).