Volume 5 • Issue 1 | March 2021
Why quadratic log-log dependence is ubiquitous and what next
Sean R. Aguilar, Vladik Kreinovich, Uyen Pham
Abstract:
Purpose – In many real-life situations ranging from financial to volcanic data, growth is described either by a power law – which is linear in log-log scale or by a quadratic dependence in the log-log scale. The purpose of this paper is to explain this empirical fact.
Design/methodology/approach – The authors use natural scale invariance requirements.
Findings – In this paper, the authors used natural scale invariance requirement to explain the ubiquity of quadratic log-log dependencies. The authors also explain what to do if quadratic log-log models turn out to be insufficiently accurate. In this case, scale invariance requirements lead to dependencies which in the log-log scale take cubic, 4th order, etc. form.
Originality/value – To the best of authors’ knowledge, this is the first theoretical explanation of the empirical quadratic log-log dependence.
References:
- Aczél, J. and Dhombres, J. (2008), Functional Equations in Several Variables, Cambridge University Press.
- Mariani, M.C., Asante, P.K., Bhuyian, M.A.M., Beccar-Varela, M.P., Jaroszewicz, S. and Tweneboah, O.K. (2020), “Long-range correlations and characterization of financial and volcanic time series”, Mathematics, Vol. 8 No. 3, pp. 441.