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Benford's law is a simple empirical tested first digit distribution in data series.

I do my Macroeconomics Thesis and I am going to propose to evaluate various filtering processes. I have found an IMF article where they use the first digit law to evaluate data quality and it applies in EU12 and other developed countries.

My hypothesis is the following: if benford's law applies on raw data, then it should apply if the filter just denoises and keep intact the information. If it does not apply something is going on and needs to be examined.

However, I just realised that filtering (e.g wavelets) will detrend my signals, therefore it doesn't make sense to me to use benford's law after the process, because it examines the first digits' distribution with trend. Do you see any way to apply this and more importantly, is my hypothesis valid in first place?

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    This is another question that might get some good answers on stats (dot) stackexchange (dot) com that it might not get here. – 2017-02-15
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    @michael Yesterday night I found some very intresting results on my question. I will rephrase it as soon as I can. The first digit phenomenon is under the umbrella of number theory, so I am going to fix the question to be related to math. – 2017-02-15

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