MCN-1 Invariants and Homomorphisms Implicit in, and the Irrelevance of the Mean-Variance Framework
20 Pages Posted: 17 Dec 2007 Last revised: 14 Nov 2015
Date Written: 2015
Many aspects of modern statistical analysis are based almost entirely on the mean-variance framework and its elements – variance, semi-variance, correlation and Covariance. Unfortunately, these measures are very inaccurate and don’t reflect the realities of phenomena, and are also theoretically inappropriate. This article introduces Invariants for analysis of rates-of-change and Pattern-Formation; and illustrates the many problems inherent in, and clarifies the Mean-Variance (M-V) framework. That is, some of the illustrated limitations of the M-V Framework are Invariants that present new opportunities in computing and computational methods in various fields including Pattern-Formation, Chaos and Evolutionary Computation, given the discussions in Sandfeld & Zaiser (2015); Kriener, Helias, Rotter, et. al. (2014); Fenn, et al. (2011); Preis, Kenett, et. al. (2012). Kriener, Helias, Rotter, et. al. (2014); Kenett, et.al. (2012); Pearson (1895); Fuwape & Ogunjo (2013); Menna, Rotundo & Tirozzi (2002); and Andrade, Ribeiro & Rosa (2006), all of which omitted the limitations.
Keywords: Correlation, Covariance, Variance, Semi-Variance, Volatility, Risk Analysis, mechanics, Portfolio Management
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