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Yarahmadi H, Saberi AA. A 2D Lévy-flight model for the complex dynamics of real-life financial markets. CHAOS (WOODBURY, N.Y.) 2022; 32:033113. [PMID: 35364828 DOI: 10.1063/5.0082926] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2021] [Accepted: 02/23/2022] [Indexed: 06/14/2023]
Abstract
We report on the emergence of scaling laws in the temporal evolution of the daily closing values of the S&P 500 index prices and its modeling based on the Lévy flights in two dimensions (2D). The efficacy of our proposed model is verified and validated by using the extreme value statistics in the random matrix theory. We find that the random evolution of each pair of stocks in a 2D price space is a scale-invariant complex trajectory whose tortuosity is governed by a 2/3 geometric law between the gyration radius Rg(t) and the total length ℓ(t) of the path, i.e., Rg(t)∼ℓ(t)2/3. We construct a Wishart matrix containing all stocks up to a specific variable period and look at its spectral properties for over 30 years. In contrast to the standard random matrix theory, we find that the distribution of eigenvalues has a power-law tail with a decreasing exponent over time-a quantitative indicator of the temporal correlations. We find that the time evolution of the distance of 2D Lévy flights with index α=3/2 from origin generates the same empirical spectral properties. The statistics of the largest eigenvalues of the model and the observations are in perfect agreement.
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Affiliation(s)
- Hediye Yarahmadi
- Department of Physics, University of Tehran, P. O. Box 14395-547, Tehran, Iran
| | - Abbas Ali Saberi
- Department of Physics, University of Tehran, P. O. Box 14395-547, Tehran, Iran
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Koohi Lai Z, Namaki A, Hosseiny A, Jafari G, Ausloos M. Coupled Criticality Analysis of Inflation and Unemployment. ENTROPY (BASEL, SWITZERLAND) 2020; 23:E42. [PMID: 33396720 PMCID: PMC7824125 DOI: 10.3390/e23010042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/08/2020] [Revised: 12/01/2020] [Accepted: 12/07/2020] [Indexed: 11/17/2022]
Abstract
In this paper, we focus on the critical periods in the economy that are characterized by unusual and large fluctuations in macroeconomic indicators, like those measuring inflation and unemployment. We analyze U.S. data for 70 years from 1948 until 2018. To capture their fluctuation essence, we concentrate on the non-Gaussianity of their distributions. We investigate how the non-Gaussianity of these variables affects the coupling structure of them. We distinguish "regular" from "rare" events, in calculating the correlation coefficient, emphasizing that both cases might lead to a different response of the economy. Through the "multifractal random wall" model, one can see that the non-Gaussianity depends on time scales. The non-Gaussianity of unemployment is noticeable only for periods shorter than one year; for longer periods, the fluctuation distribution tends to a Gaussian behavior. In contrast, the non-Gaussianities of inflation fluctuations persist for all time scales. We observe through the "bivariate multifractal random walk" that despite the inflation features, the non-Gaussianity of the coupled structure is finite for scales less than one year, drops for periods larger than one year, and becomes small for scales greater than two years. This means that the footprint of the monetary policies intentionally influencing the inflation and unemployment couple is observed only for time horizons smaller than two years. Finally, to improve some understanding of the effect of rare events, we calculate high moments of the variables' increments for various q orders and various time scales. The results show that coupling with high moments sharply increases during crises.
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Affiliation(s)
- Zahra Koohi Lai
- Department of Physics, Islamic Azad University, Firoozkooh Branch, Firoozkooh 3981838381, Iran;
| | - Ali Namaki
- Department of Finance, Faculty of Management, University of Tehran, Tehran 1411713114, Iran
- Iran Finance Association, Tehran 1411713114, Iran
| | - Ali Hosseiny
- Department of Physics, Shahid Beheshti University, Tehran 1983969411, Iran; (A.H.); (G.J.)
| | - Gholamreza Jafari
- Department of Physics, Shahid Beheshti University, Tehran 1983969411, Iran; (A.H.); (G.J.)
- Center for Network Science, Central European University, 1051 Budapest, Hungary
| | - Marcel Ausloos
- School of Business, College of Social Sciences, Arts, and Humanities, Brookfield, University of Leicester, Leicester LE2 1RQ, UK;
- Group of Researchers for Applications of Physics in Economy and Sociology (GRAPES), Rue de la belle jardinière, 483, Sart Tilman, Angleur, B-4031 Liege, Belgium
- Department of Statistics and Econometrics, Bucharest University of Economic Studies, Calea Dorobantilor 15–17, Sector 1, 010552 Bucharest, Romania
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