Fred Viole

Using partial moments, the authors introduce a new toolbox of statistical tools. The advantage of using partial moments is that it is nonparametric and does not require the knowledge of the underlying probability function nor does it require a "goodness of fit" analysis. Partial moments provide us with cumulative density functions, probability density functions, linear correlation and regression analysis, nonlinear correlation and regression analysis, ANOVA, and ARMA/ARCH models. One major advantage with this work is that the partial moment methodology fully replicates linear conditions or known functions. This trust of methodology is important for transition to chaotic unknowns and forecasting with autoregressive models. Linearity should be a pleasant surprise to encounter in data, not a prerequisite. By eliminating all preconceptions and assumptions, we offer a powerful framework for statistical analysis. The simple nonparametric architecture based on partial moments yields important information to easily conduct multivariate analysis; generating descriptive and inferential statistics for a nonlinear world.

The authors begin by re-examining utility theory in order to establish a stable foundation to their work in risk quantification and a markets hypothesis. This fresh perspective offers a truly heterodox methodology, abandoning the assumptions economic and financial theory have depended on for decades. Introducing the updated utility theory into post modern portfolio theory has enabled the authors to demonstrate ex ante efficiency, rather than ex post optimization. The current financial crisis, as well as historical ones, could have been avoided if market participants had a better theoretical framework from which to operate. This work offers such a framework with the guiding principle that the inherent uncertainty of markets cannot be modeled away with convenient assumptions.