Gaussian Vs Stable distribution

["Walter Lake" <wlake@xxxxxxxxx>]

Thanks for your email.

The histogram on page 86 of the Dec. 99 TASC "Trade Against the Gap" is
typical of a normal or Gaussian distribution. That is the typical
distribution that descriptive stats works with or assumes. Most momentum and
trend studies are based on the linearity implied in the normal distribution.
The tails of curve normally "touch down" at +2 and -2 standard deviation or
sigma. Therefore implying a nice "safe" compact base of data or trades.

When dealing with time series data you might want to go one step farther and
look at non-linearity and Stable distribution curves. They are usually
"higher" and "thinner" and normally have "room to spare" at sigma 2 for
extensions out to sigma 3, 4, and 5. These are the inefficiencies that
really make the money or put you out of business. The studies developed from
them are persistence studies which are different from momentum and trend
studies. One popular indicator of persistence is the Hurst Exponent. (See
Christopher May's books or articles).

Since you are working with stocks or indexes you might want to consider
looking at those.  Several traders that I know are out of the business now
because of sigma 4 and 5 events.

Best regards

Walter