Financial Data Analysis

This set of web pages is dedicated to novel methods with which to examine and understand financial data. The site is under development and evolving, as are many of the ideas presented here. The web pages were all created with Mathematica notebooks, some of which were initially introduced on the mathestate website.

As pages are added, they will be indexed here. By clicking on links below an html version of a Mathematica notebook will be accessed. The links are viewable in web browsers, including those on mobile devices such as the iPad and Android phones. For Mathematica users the notebooks may be accessed directly.

As the site grows, the plan is to add interactive features which can be accessed using the free Wolfram CDF Player.

The links are presented in a logical order to develop evolving ideas, but each page should be able to stand alone. As the site evolves there will be cross-links between pages, but initially this page may be the best place to start.

Extends a simple exponential growth model to sequences of financial prices. A model of normally distributed logarithmic returns is demonstrated.

27 Oct 13

Looks at the time-series of the S&P 500 index since 1950 and examines nature of the distribution of log returns for this sequence. Including a stable distribution fit and the distribution tail behavior.

27 Oct 13

Looks at Student T distribution fit to the S&P 500 log return series.

27 Oct 13

This is an in depth look at a non-stationary model of a stable distribution with varying scale factor, which has serial dependence.

27 Oct 13

A thought experiment to explain the origin of power-tail behavior found in stock market logarithmic returns.

29 Oct 13

This notebook shows some fits of intraday data to the stable 2:3 order statistic distribution at the one minute level.

31 Oct 13

A model for the price structure of zero coupon Treasury bonds is based on the survival function of a probability distribution arising from the sum of an exponential distribution random variable and a gamma distribution random variable. The three-parameter function is used to fit prices of zero coupon treasury bonds with respect to their time to maturity with excellent results.

26 Nov 13

A fifty year history of the FOMC activity and the relation to recessions, using a model for bond price structure based on the solution to an ordinary differential equation.

22 Jan 14

FFT for Probability Calculations

The fast Fourier transform and the stable 2:3 order statistic distribution model for financial returns are combined to create monthly probability calculations from a daily data time series.

28 May 14

Maximum likelihood fits are graphically compared for ten year and two year data sets to the stable 2:3 order statistic distribution and the Student T distribution.

30 May 14

The links above provide an overview of the structure of financial behavior derived from daily closing prices.

Other topics listed below will gradually be added.

TreasuryZeroesODE

A model for the price structure of zero coupon Treasury bonds based on the solution of an ordinary differential equation.

HighFrequencyData

A look at transaction by transaction data.

StableOrderDistributions

Exploration of the order statistic distributions of stable distributions. Some have an attractive tail behavior which is matched to financial data.

TailBehavior

VolatilityTrends

Comments and suggestions are welcome: rimmer367@outlook.com.

© Copyright 2014 Robert H. Rimmer, Jr. Fri 30 May 2014