Benford's laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity

Journal article

Ausloos, M, Ficcadenti, V, Dhesi, G and Shakeel, M (2021). Benford's laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity. Physica A: Statistical Mechanics and its Applications. 574, pp. 125969-125969. https://doi.org/10.1016/j.physa.2021.125969
AuthorsAusloos, M, Ficcadenti, V, Dhesi, G and Shakeel, M
Abstract

The so-called Benford's laws are of frequent use to detect anomalies and regularities in data sets, particularly in election results and financial statements. However, primary financial market indices have not been much studied, if studied at all, within such a perspective. This paper presents features in the distributions of S&P500 daily closing values and the corresponding daily log-returns over a long time interval, [03/01/1950 - 22/08/2014], amounting to 16265 data points. We address the frequencies of the first, second, and first two significant digits and explore the conformance to Benford's laws of these distributions at five different (equal size) levels of disaggregation. The log-returns are studied for either positive or negative cases. The results for the S&P500 daily closing values are showing a remarkable lack of conformity, whatever the different levels of disaggregation. The causes of this non-conformity are discussed, pointing to the danger in taking Benford's laws for granted in large databases, whence drawing “definite conclusions”. The agreements with Benford's laws are much better for the log-returns. Such a disparity in agreements finds an explanation in the data set itself: the index's inherent trends. To further validate this, daily returns have been simulated via the Geometric Brownian Motion and calibrating the simulations with the observed data averages and testing against Benford's laws when the log-returns distribution's standard deviation changes. One finds that the trend and the standard deviation of the distributions are relevant parameters in concluding about conformity with Benford's laws.

Year2021
JournalPhysica A: Statistical Mechanics and its Applications
Journal citation574, pp. 125969-125969
PublisherElsevier BV
ISSN0378-4371
Digital Object Identifier (DOI)https://doi.org/10.1016/j.physa.2021.125969
Publication dates
Print15 Jul 2021
Online29 Mar 2021
Publication process dates
Accepted29 Mar 2021
Deposited21 Apr 2021
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James, SL, Abate, D, Abate, KH, Abay, SM, Abbafati, C, Abbasi, N, Abbastabar, H, Abd-Allah, F, Abdela, J, Abdelalim, A, Abdollahpour, I, Abdulkader, RS, Abebe, Z, Abera, SF, Abil, OZ, Abraha, HN, Abu-Raddad, LJ, Abu-Rmeileh, NME, Accrombessi, MMK, Acharya, D, Acharya, P, Ackerman, IN, Adamu, AA, Adebayo, OM, Adekanmbi, V, Adetokunboh, OO, Adib, MG, Adsuar, JC, Afanvi, KA, Afarideh, M, Afshin, A, Agarwal, G, Agesa, KM, Aggarwal, R, Aghayan, SA, Agrawal, S, Ahmadi, A, Ahmadi, M, Ahmadieh, H, Ahmed, MB, Aichour, AN, Aichour, I, Aichour, MTE, Akinyemiju, T, Akseer, N, Al-Aly, Z, Al-Eyadhy, A, Al-Mekhlafi, HM, Al-Raddadi, RM, Alahdab, F, Alam, K, Alam, T, Alashi, A, Alavian, SM, Alene, KA, Alijanzadeh, M, Alizadeh-Navaei, R, Aljunid, SM, Alkerwi, A, Alla, F, Allebeck, P, Alouani, MML, Altirkawi, K, Alvis-Guzman, N, Amare, AT, Aminde, LN, Ammar, W, Amoako, YA, Anber, NH, Andrei, CL, Androudi, S, Animut, MD, Anjomshoa, M, Ansha, MG, Antonio, CAT, Anwari, P, Arabloo, J, Arauz, A, Aremu, O, Ariani, F, Armoon, B, Ärnlöv, J, Arora, A, Artaman, A, Aryal, KK, Asayesh, H, Asghar, RJ, Ataro, Z, Atre, SR, Ausloos, M, Avila-Burgos, L, Avokpaho, EFGA, Awasthi, A, Ayala Quintanilla, BP, Ayer, R, Azzopardi, PS, Babazadeh, A, Badali, H, Badawi, A and Bali, AG (2018). Global, regional, and national incidence, prevalence, and years lived with disability for 354 Diseases and Injuries for 195 countries and territories, 1990-2017: A systematic analysis for the Global Burden of Disease Study 2017. The Lancet. 392 (10159), pp. 1789-1858. https://doi.org/10.1016/S0140-6736(18)32279-7
Non stationarity of high order return distribution moments and their Irrational fractional Brownian Motion modelling
Dhesi, G (2018). Non stationarity of high order return distribution moments and their Irrational fractional Brownian Motion modelling. EURO 2018. Valencia 08 - 11 Jul 2018
Comparative Causality Analyses between Hydrological Natural Inflow and Climate Variables in Brazil
Huang, X, Macaira, P, Hassani, H, Oliviera, F and Dhesi, G (2018). Comparative Causality Analyses between Hydrological Natural Inflow and Climate Variables in Brazil. Physica A: Statistical Mechanics and its Applications. 516, pp. 480-495. https://doi.org/10.1016/j.physa.2018.09.079
Quantitative and qualitative analysis of editor behavior through potentially coercive citations
Herteliu, C, Ausloos, M, Ileanu, BV, Rotundo, G and Andrei, T (2017). Quantitative and qualitative analysis of editor behavior through potentially coercive citations. Publications. 5 (2), pp. 15-15. https://doi.org/10.3390/publications5020015
Earthquakes economic costs through rank-size laws
Ficcadenti, V and Cerqueti, R (2017). Earthquakes economic costs through rank-size laws. Journal of Statistical Mechanics: Theory and Experiment. 2017 (8), pp. 083401-083401. https://doi.org/10.1088/1742-5468/aa7ab7
Decomposition of the Inequality of Income distribution by income types- Application for Romania
Andrei, T, Oancea, B, Richmond, P, Dhesi, G and Herteliu, C. (2017). Decomposition of the Inequality of Income distribution by income types- Application for Romania. Entropy. 19 (9), p. 430. https://doi.org/10.3390/e19090430
Modelling and measuring the irrational behaviour of agents in financial markets: Discovering the psychological soliton
Dhesi, G and Ausloos, M (2016). Modelling and measuring the irrational behaviour of agents in financial markets: Discovering the psychological soliton. Chaos, Solitons and Fractals. 88 (July), pp. 119-125. https://doi.org/10.1016/j.chaos.2015.12.015
Modified Brownian Motion Approach to Modelling Returns Distribution
Dhesi, G, Shakeel, MB and Xiao, L (2016). Modified Brownian Motion Approach to Modelling Returns Distribution. Wilmott. 82, pp. 74-77. https://doi.org/10.1002/wilm.10494
Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices
Dhesi, G and Ausloos, M (2016). Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 93 (6). https://doi.org/10.1103/PhysRevE.93.062115