If Not Normal then What

Published earlier on blog.gillerinvestments.com

In the previous post we illustrated the evident abnormality of financial data by examining the longitudenal returns of the S&P 500 Index.

I used the Generalized Error Distribution as it possesses the ability to be smoothly transformed from a Normal Distribution into a leptokurtotic distribution and that allowed me to use the Maximum Likelihood Ratio Test to distinguish between the null hypothesis (that the data is I.I.D. Normal) and the alternate hypothesis (that it is not).

I subscribe to the theory that if something is right you should be able to draw the same conclusions via various methods and data sets. So I am going to look again at the likely models for the innovations of financial data (we're taking a GARCH(1,1) model as given); but, this time, I decided to look at the S&P Goldman Sachs Commodity Index and to use a test based on Pearson's χ² Test. (In the following the data is actually based on the first deliverable contract on the GSCI traded at the CME.)

Before that, however, we should discuss what the possible options are the for the PDF of the process innovations. The candidates are:

• The Normal Distribution


• Levy Flight


• The Generalized Error Distribution


• Student's t Distribution


• something else…

Continued…