From: John Conover <john@email.johncon.com>

Subject: Re: Fractal "bubbles", Re: Business News from Wired News, and Re: Positive & Negative Bubbles in Asian Markets

Date: 13 Feb 1999 05:14:55 -0000

John Conover writes: > > Hi Burkhard. There is a graph that tends to support your conclusions at: > > http://www.johncon.com/john/correspondence/981230002304.31518.html > > It would appear that the duration of "bubbles" in the US equity > markets do follow a 1 / sqrt (t) scenario. The magnitude of the > "bubbles" seem to be proportional to the sqrt (t). I have a graph of > that, if you would like me to put it on the site. > The above URL/page is a graph of the run lengths of US equity market expansions and contractions, (ie., "bubbles",) for the last 27 years-the data includes the the DJIA, NYSE, and the S&P 500, by the day, a simulated fractal, (made with the tsfBm program, using a 60% persistence,) and, by comparison, the run lengths for a theoretical random walk fractal. Attached is a graph of the magnitude of the run lengths, using the same data, and the magnitude for a theoretical random walk fractal. The graph covers "bubbles" of less than 500 trading days duration, (about 2 calendar years.) The way you use it, for example, is to find the magnitude of a "bubble" at 100 days into the "bubble" (on the x-axis,) which would have a standard deviation of about 0.1, on the y-axis. What this means is that there is an 84.135%, (ie., one standard deviation,) chance that the magnitude of a "bubble" will be less than 0.1, or 10%. Likewise, there is a 15.865% chance, that it will be larger than 10%. For example, if an equity index value was 100 when the "bubble" started, then there is an 84% chance that the value of the index, 100 days later, will be less than 110, and a 16% chance that it will be more. John

-- John Conover, john@email.johncon.com, http://www.johncon.com/

Copyright © 1999 John Conover, john@email.johncon.com. All Rights Reserved. Last modified: Fri Mar 26 18:52:48 PST 1999 $Id: 990212211510.16959.html,v 1.0 2002/02/12 19:54:06 conover Exp $