Fred Viole's Research

Fred Viole's Research

Partial Moments

f(Newton)

Cumulative Distribution Functions and

UPM/LPM Analysis

ANOVA Using Continuous Cumulative Distribution Functions

“f(Newton)” explains what partial moments are. It demonstrates how to approximate an area of an integral of a function. It is not the exact area we find from the antiderivative of the function, rather it is the antiderivative divided by the interval. Partial moments converge to this measurement as the number of observations increase. This has the inherent benefit of avoiding specifying the function as required with traditional calculus.

“Cumulative Distribution Functions and UPM/LPM Analysis” explains how partial moments are the elements of variance. This paper identifies all of the interaction matrices and then aggregates them into the variance/covariance matrix. These interactions can be analyzed to derive how variables' relationship, instead of drawing straight lines on a joint distribution (like Pearson’s correlation, PCA, linear regression, etc). Traditional σ-based statistics are incapable of differentiating between positive and negative variance, but for finance, these insights are instrumental in applying utility theory.

https://www.scribd.com/doc/123972410/f-Newton-pdf

Analysis of Variance (ANOVA) is a statistical method used to determine whether a sample originated from a larger population distribution. We provide an alternate method of determination using the continuous cumulative distribution functions derived from degree one lower partial moment ratios. The resulting analysis is performed with no restrictive assumptions on the underlying distribution or the associated error terms.

https://www.scribd.com/doc/155403103/ANOVA-Using-Continuous-Cumulative-Distribution-Functions

Options Theory in an Upper and Lower Partial Moment Fabric

Black-Scholes-Merton was the default method of options pricing after its introduction in 1973. However, prices are no longer set by the method, rather market prices are backwardly induced into the model to derive volatility estimates for the underlying. The existence of the volatility smile empirically rejects the notion of a static underlying volatility estimate per Black-Scholes-Merton. The volatility estimate is where we focus our attention, incorporating an upper partial moment for calls and a lower partial moment for puts.

Nonlinear Nonparametric Statistics

Behavioral

Finance

Ambiguity

Aversion

Autoregressive Modeling

Puzzles and Paradoxes: The Consistent Role of Ambiguity Aversion

Deriving Nonlinear Correlation Coefficients from Partial Moments

This paper makes a first step at a periodic table of sorts to reduce the myriad of behavioral biases noted. When classifying these anomalies into similar structural ambiguities we note the consistency of individuals' distaste for ambiguity.

The Equity Premium Puzzle: Defining a Robust Risk Aversion Coefficient

We are able to demonstrate forecasting ability with none of the requirements of the traditional ARMA method, while strictly adhering to the definition of an autoregressive model. We also propose a new test for seasonality using coefficient of variance comparisons for component series, and then extend this proposed method to non-seasonal data. The resulting effect is that of conditional heteroskedasticity on the forecast with more accurate forecasts derived from implementing nonlinear regressions into the component series.

LPM Density Functions for the Computation of the SD Efficient Set

https://www.scribd.com/doc/128650070/Puzzles-and-Paradoxes

By using ambiguity parameters in a risk aversion coefficient we are able to easily justify the risk levels required to solve this problem. We note evidence of these levels of risk and simultaneously apply it to the risk-free rate puzzle with similar success.

“Deriving Nonlinear Correlation Coefficients from Partial Moments” is a specific application of the elements of variance in performing correlation and regression analysis. We can imitate traditional metrics using mean targets or realize further insight from different targets (such as 0) to answer “how often” and “to what extent” variables interact. Each specific element’s properties serve as regression points which enable a nonlinear structure similar to a local means methodology.

https://www.scribd.com/doc/85393819/EPP-Solution

Utility Theory

We present a test for first, second, and third degree stochastic dominance between two variables using Lower Partial Moments. And we provide an algorithm for efficiently determining stochastic dominance efficient sets among large numbers of variables.

Nonparametric Regression Using Clusters

https://www.scribd.com/doc/140999751/Non-Linear-Correlation-Coefficients

We compare two nonlinear regression estimation packages called ‘NNS’, Viole (NNS: nonlinear non-parametric statistics, 2016), and ‘np’, Hayfield and Racine (J Stat Softw 27(5):1–32,2008), with the help of a simulation using deterministic (DT) and stochastic (ST) regressor models. We find the respective coefficients of determination (R2) are close for DT models, while finding an advantage to NNS in ST and large sample cases.Regression coefficients are sometimes regarded as approximations to partial derivatives, especially in social sciences. Then, NNS alone has the ability to compute a range of partials evaluated at points within the sample and also out-of-sample. Thus NNS can provide a viable alternative to kernel based nonparametric regressions without using bandwidths for smoothing.

Nonlinear Scaling Normalization with Variance Retention

Predicting Risk-Return Performance Using UPM-LPM Metrics

Beyond Correlation

Embracing the Cognitive Dissonance Between Expected Utility Theory and Prospect Theory

http://rdcu.be/tz0J

The Utility of Wealth in an Upper and Lower Partial Moment Fabric

This paper provides an empirical test to our normative and mathematical utility work. We do find subjective wealth to be the determinant of decisions under uncertainty. We also note the use of benchmarks consistent with the previous works' wealth proxy suggestions. This work enables a methodology in determining an individual's risk profile to be integrated via the partial moment framework in portfolio construction.

This normative utility work explores the notion of two utility functions, one for losses and one for gains. We create a four-fold function accounting for all behaviors noted in Prospect Theory and also illustrate how the Prospect Theory value function is embedded within the overall function.

The goal of this work was to show "a" not "the" way to predicting individual security performance. We compared our method versus classical optimized methods and handily outperformed them. It is counter-intuitive to the explain -> predict paradigm, but has a theoretical foundation based on information theory while using the inherent flexibility afforded by partial moments.

We present a nonlinear method of scaling to achieve normalization of multiple variables. We compare this method to the standard linear scaling and the quantile normalization methods. We find our overall normalized distribution to be more representative of the original data set with regards to standard moments of individual variables. We also find our normalized results to have an overall lower standard deviation versus both the linear scaling and quantile normalization results for variables with similar distributions.

"Beyond Correlation" identifies the dependence structure between variables through further quadrant analysis . It also identifies the conflicting correlation concerns inherent in MPT mean/variance optimization. Finally, it demonstrates a true 3D correlation coefficient.

https://www.scribd.com/doc/106306706/Embracing-the-Cognitive-Dissonance-Between-Expected-Utility-Theory-and-Prospect-Theory

https://www.scribd.com/doc/80574232/The-Utility-of-Wealth-in-an-Upper-and-Lower-Partial-Moment-Fabric

An Analysis of Heterogeneous Utility Benchmarks in a Zero Return Environment

A Note on Stochastic Dominance

Clustering and Curve Fitting by Line Segments

This mathematical treatment of our normative utility function demonstrates how historical utility functions break down for a zero return. It also illustrates the effects of different benchmarks on the overall utility function and how they proxy the subjective wealth of the individual.

https://www.scribd.com/doc/155403994/Non-Linear-Scaling-Normalization-With-Variance-Retention

This note is to set the record straight and focus on the strict definition of stochastic dominance.

https://www.scribd.com/doc/233825010/Predicting-Risk-Return-Performance-Using-UPM-LPM-Metrics

https://www.scribd.com/doc/236902020/Beyond-Correlation

Behavioral finance in financial market theory, utility theory, portfolio theory and the necessary statistics: A review

https://www.scribd.com/doc/83244534/An-Analysis-of-Heterogeneous-Utility-Benchmarks-in-a-Zero-Return-Environment

Nonlinear nonparametric statistics (NNS) algorithm offers new tools for curve fitting. A relationship between k-means clustering and NNS regression points is explored with graphics showing a perfect fit in the limit. The goal of this paper is to demonstrate NNS as a form of unsupervised learning, and supply a proof of its limit condition. The procedural similarity NNS shares with vector quantization is also documented, along with identical outputs for NNS and a k nearest neighbors (kNN) classification algorithm under a specific NNS setting. Fisher's iris data and artificial data are used. Even though a perfect fit should obviously be reserved for instances of high signal to noise ratios, it permits greater flexibility by offering a large spectrum of possible fits from linear to perfect.

https://ssrn.com/abstract=3002675

Causation

https://ssrn.com/abstract=2861339

The Markets Hypothesis

PORTFOLIO

THEORY

This article provides an overview of utility theory's consistent role in finance dating back to the 1700's. We examine attempts to incorporate this important feature as well as effects from assuming it away. Furthermore, we look at philosophical deficiencies in traditional statistics which rebuke attempts to "behavioralize" them.

Classification Using NNS Clustering Analysis

The real issue is how to determine conditional probability outside of experimentation which directly controls for this. Enter normalization. Putting multiple variables on the same histogram enables the ability to view and analyze conditional probabilities. Using these insights we were able to review the convergent cross mapping method and confirm most of their findings. Also, we incorporated the sensible suggestions from Granger by normalizing the variable against lagged periods of itself to properly consider priors.

We review historical linear random walk models and other central assumptions in the Efficient Markets Hypothesis, as well as the evolution into more behavioral models such as the Adaptive Markets Hypothesis while explaining the consistencies of entropy and bifurcations. We propose new classification and weighting metrics of the participants. This market analysis focuses on the ensuing distribution of the participants corresponding with the prices for the security.

https://www.scribd.com/doc/230067430/Behavioral-finance-in-financial-market-theory-utility-theory-portfolio-theory-and-the-necessary-statistics-A-review

In 1952 Harry Markowitz put forth a solution to the portfolio selection process. He summarizes the stages and objectives with the following, “The process of selecting a portfolio may be divided into two stages. The first stage starts with observation and experience and ends with beliefs about the future performances of available securities. The second stage starts with the relevant beliefs about future performances and ends with the choice of portfolio.”

We offer a complimentary extension of modern portfolio theory, namely the redefinition of the second stage via partial moments and the probabilistic reformulation of security analysis of the first stage via the conditioning of returns with entropy proxies.

This article is intended to present working examples of several classification problems using NNS clustering analysis.

We demonstrate how NNS clustering is quite effective, as well as an alternative method NNS employs for classification tasks. We compare predictions of test sets with NNS, k-means using the "cl.predict" routine offered in R to "predict class ids or memberships from R objects representing partitions", K nearest neighbors classification using the "knn" routine in R-package "class", and a naive Bayes classification using the "e1071" package.

https://www.scribd.com/doc/128661289/The-Markets-Hypothesis

https://www.scribd.com/doc/155404418/Causation

https://ssrn.com/abstract=2864711