Benford’s law and Theil transform of financial data

Abstract

Among econophysics investigations, studies of religious groups have been of interest. On one hand, the present paper concerns the Antoinist community financial reports, -a community which appeared at the end of the 19-th century in Belgium. Several growth-decay regimes have been previously found over different time spans. However, there is common suspicion about sect finances. In that spirit, the Antoinist community yearly financial reports, income and expenses, are hereby examined along the so-called Benford's law. The latter is often used as a test about possible accounting wrongdoings. On the other hand, Benford's law is known to be invariant under scale and base transformation. Therefore, as a further test, of both such data and Benford's law use, the yearly financial reports are nonlinearly remapped through a sort of Theil transformation, i.e. based on a log-transformation. The resulting data is again analyzed along the Benford's law scheme. Bizarre, puzzling, features are seen. However, it is emphasized that such a non-linear transformation can shift the argument toward a more objective conclusion. In an Appendix, some brief discussion is made on why the original Theil mapping should not be used. In a second Appendix, an imperfect Benford's law-like form, -better suited for anomalous distributions, is presented.

The Usefulness Of Analytical Procedures, Other Than Ratio And Trend Analysis, For Auditor Decisions

“…The focus on Du Pont, EVA and Altman's Z-score is due to their importance in university syllabuses and are probably the most frequent used structured ratio analysis (Correia, Flynn, Uliana, & Wormald, 2011). Benford's Law is often used to identify accounting fraud (Clippe & Ausloos, 2012).…”

“…Benford's Law is typically utilised as a test about potential accounting misconduct (Clippe & Ausloos, 2012). Deviations from the expected Benford's Law digit distribution may indicate a higher likelihood of human interaction (Drake & Nigrini, 2000;Henselmann, Scherr, & Ditter, 2013).…”

“…The results should therefore be interpreted with care (Durtschi et al, 2004) and complementary accounting techniques should be considered before concluding whether records are forged (Clippe & Ausloos, 2012). …”

“…(Clippe & Ausloos, 2012;Poston et al, 2011). It is therefore submitted that a variety of complementary analytical procedures should be used in order to obtain a complete picture of a company's financial health reflected in financial statements.…”

On the “usual” misunderstandings between econophysics and finance: Some clarifications on modelling approaches and efficient market hypothesis

“…One can mention, among other works, Redelico et al (2009) and Gligor and Ausloos (2007) who used the Student's t-test; Clippe and Ausloos (2012) and Mir et al (2014) who used a chi-square test; and also Queiros (2005), Zanin et al (2012), Theiler et al (1992) or Morales et al (2013). However, as some econophysicists pointed out, "better and more careful testing is needed, and that too much of data analysis in this area relies on visual inspection alone" (Farmer & Geanakoplos, 2008, p. 24).…”