Could Noise Spectra of Strange Attractors Better Explained Wealth and Income Inequalities? Evidence from the S&P-500 Index.

Dominique, C-Rene (2018): Could Noise Spectra of Strange Attractors Better Explained Wealth and Income Inequalities? Evidence from the S&P-500 Index.

Abstract

SUMMARY: Inequity in wealth and income distributions is ubiquitous and persistent in markets economies. Economists have long suspected that this might be due to the workings of a power law. But studies in financial economics have focused mainly on tail exponent while attempting to recover the Pareto and Zipf’s laws. The estimation of tail exponents from log-log plots, as in stock market returns, produces biased estimators and has little impact on policy. This paper argues that economic time series are output signals of a multifractal process driven by strange attractors. Consequently, estimating noise spectra thrown-up by strange attractors stands to produce a much richer set of information, including the lower and upper bounds of unequal income distribution.

• Item Type: MPRA Paper
• Language: English
• Keywords: noise spectra, singularity spectrum, correlation dimension, income distribution, fractal attractor, scale exponent.
• Subjects: G - Financial Economics > G1 - General Financial Markets; G - Financial Economics > G1 - General Financial Markets > G14 - Information and Market Efficiency ; Event Studies ; Insider Trading

References

Alvaredo, F., Chancel, et al. (2017). “The Elephant Curve of Global Inequality and Growth.” WID.word Working Paper Series 2017/20.

Armeodo, A. et al. (1995). The thermodynamics of fractals revisited with wavelets. Physica A, 213, 232-275.

Dominique, C-R. and Rivera, S L. (2012). “Short-Term Dependence in Time Series as an Index of Complexity: Example from the S&P-500 Index.” International Business Research, 5, 38-47.

Dominique, C-R. (2017). “On the Scientificity of Microeconomics: Individual Demand and Exchange-Value Determination.” Theoretical and Practical Research in Economic Field, VIII, 2, 106-110.

Frisch, U. (1995). Turbulence. Cambridge University Press: Cambridge.

Gabais, X. (1999). “Zipf’s Law for Cities: An Explanation.” Quarterly Journal of Economics. 114, 739-767.

Gabais, X., Gopikrishnan, P. et al. (2003). “A Theory of Power Law Distributions in Financial Market Fluctuations.” Nature, 423, 267-330.

Gopikrisnan, P, Plerou, U. et al. (2000). “Statistical Properties of Share Volume.” Traded in Financial Markets.” Physical Review E, 62, R4403-96.

Grassberger, Peter (1981). On the Hausdorff dimension of fractal attractors. Journal of Statistical Physics, 26, 173-179.

Grassberger, Peter & Procaccia, I. (1983). Characterization of strange attractors. Physical Review Letters, 50, 346-349.

Koulakis, B. Ruseckas, J. et al. (2006). “Non-Linear Stochastic Models of 1/f Noise and Power Law Distribution.” Physica A, 365-397.

Maio, Y., Ren, W. and Ren, Z. “On the Fractional Mixed Brownian Motion.” Applied Mathematical Science, 35, 1759-1738.

Mandelbrot, B. & van Ness, J., W. (1968). Fractional Brownian motions, fractional noises and applications. SIAM Review, 10, 422-437.

Mandelbrot, B. (1974). “Intermittent turbulence in self-similar cascades: Divergence of high moments and dimension of the carrier. Journal of Fluid Mechanics, 62, 331-358.

Mandelbrot, B. (1982). The Fractal Geometry of Nature, New York: W. H. Freeman.

Mandelbrot, B. (2003). Multifractal Power law Distributions: Negative and Critical Dimensions and Other Anomalies, Explained by s Simple Example.” Journal of Statistical Physics, 110, (3-6), 739-774.

Medio, Alfredo (1992(. Chaotic dynamics: Theory and applications to economics. Cambridge University Press: Cambridge, uk.

Peters, Edgar (1991). A chaotic attractor for the S&P-500. Financial Analyst Journal, March/April.

Sottinen, T. (2003). Fractional Brownian motion in finance and queuing. (Doctoral dissertation, University of Helsinki, Finland, 2003).

Rasband, S. N. (1990). Fractal Dimensions” in Chaotic Dynamics of Non-linear Systems. New York: Wiley, 71-83.

Renyi, A. (1970). Probability Theory. North-Holland: Amsterdam.

Schroeder, Manfred (2009). Fractals, Chaos, Power Laws, Dover Pub., Inc.: New York.

Thale, C. (2009). Further remarks on mixed fractional Brownian motion. Applied Mathematical Sciences, 3, 1-17.

Warwick. Ac.uk (2012). Lectures on fractals and dimension theory. Homepages. warwick.ac. uk/mas dbl/dimension-total.pdf.

West, B., J. and Shlesinger, M. F. (1990). “The Noise in Natural Phenomena.” American Scientist, 78, 40-45.

Zili, M. (2006). On the mixed fractional Brownian motion. Journal. of Applied Mathematics and Stochastic Analyses, 2006, 1-9.