Dominique, CRene (2018): Could Noise Spectra of Strange Attractors Better Explained Wealth and Income Inequalities? Evidence from the S&P500 Index.

PDF
MPRA_paper_84182.pdf Download (595kB)  Preview 
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 loglog 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 thrownup 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 

Original Title:  Could Noise Spectra of Strange Attractors Better Explained Wealth and Income Inequalities? Evidence from the S&P500 Index. 
English Title:  Could Noise Spectra of Strange Attractors Better Explained Wealth and Income Inequalities? Evidence from the S&P500 Index. 
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 
Item ID:  84182 
Depositing User:  CRene Dominique 
Date Deposited:  26 Jan 2018 10:14 
Last Modified:  26 Jan 2018 10:15 
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, 232275. Dominique, CR. and Rivera, S L. (2012). “ShortTerm Dependence in Time Series as an Index of Complexity: Example from the S&P500 Index.” International Business Research, 5, 3847. Dominique, CR. (2017). “On the Scientificity of Microeconomics: Individual Demand and ExchangeValue Determination.” Theoretical and Practical Research in Economic Field, VIII, 2, 106110. Frisch, U. (1995). Turbulence. Cambridge University Press: Cambridge. Gabais, X. (1999). “Zipf’s Law for Cities: An Explanation.” Quarterly Journal of Economics. 114, 739767. Gabais, X., Gopikrishnan, P. et al. (2003). “A Theory of Power Law Distributions in Financial Market Fluctuations.” Nature, 423, 267330. Gopikrisnan, P, Plerou, U. et al. (2000). “Statistical Properties of Share Volume.” Traded in Financial Markets.” Physical Review E, 62, R440396. Grassberger, Peter (1981). On the Hausdorff dimension of fractal attractors. Journal of Statistical Physics, 26, 173179. Grassberger, Peter & Procaccia, I. (1983). Characterization of strange attractors. Physical Review Letters, 50, 346349. Koulakis, B. Ruseckas, J. et al. (2006). “NonLinear Stochastic Models of 1/f Noise and Power Law Distribution.” Physica A, 365397. Maio, Y., Ren, W. and Ren, Z. “On the Fractional Mixed Brownian Motion.” Applied Mathematical Science, 35, 17591738. Mandelbrot, B. & van Ness, J., W. (1968). Fractional Brownian motions, fractional noises and applications. SIAM Review, 10, 422437. Mandelbrot, B. (1974). “Intermittent turbulence in selfsimilar cascades: Divergence of high moments and dimension of the carrier. Journal of Fluid Mechanics, 62, 331358. 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, (36), 739774. Medio, Alfredo (1992(. Chaotic dynamics: Theory and applications to economics. Cambridge University Press: Cambridge, uk. Peters, Edgar (1991). A chaotic attractor for the S&P500. 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 Nonlinear Systems. New York: Wiley, 7183. Renyi, A. (1970). Probability Theory. NorthHolland: 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, 117. Warwick. Ac.uk (2012). Lectures on fractals and dimension theory. Homepages. warwick.ac. uk/mas dbl/dimensiontotal.pdf. West, B., J. and Shlesinger, M. F. (1990). “The Noise in Natural Phenomena.” American Scientist, 78, 4045. Zili, M. (2006). On the mixed fractional Brownian motion. Journal. of Applied Mathematics and Stochastic Analyses, 2006, 19. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/84182 