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

Subject: Re: Will the stock market

Date: 5 Feb 1999 19:33:36 -0000

Bill Terrell writes: > conover@netcom.com wrote: > > > One of the advantages of using a random walk fractal as a first order > > approximation for equity values is that the assumption can be > > verified, emperically-just subtract yesterday's value from today's, > > for all days, and assemble the results into a frequency > > distribution. Its a very nice Gaussian distribution, as expected-for > > all stocks through the century, by the day. The data for all stocks is > > available on CD. > > There are those who intelligently argue a fractal model which is distinctly > non-random-walk and non-normal in its distribution, including no less than Benoit B. > Mandelbrot; see this month's (February) issue of Scientific American. Oh, sure, Bill. But as a first order approximation, a random walk is pretty good, (depending on who is telling the story, of course.) There is a graph of the distributions of the daily marginal increments of the DJIA, NYSE, and S&P 500, for 27 years at: http://www.johncon.com/john/correspondence/981229233103.31169.html and it does seem to indicate, as you suggest, that there is a slight persistence in equity indices. A random walk has statistically independent increments-ie., a 50/50 chance that the next increment will be like the previous increment. The indices, however, seem to have about a 60% chance-meaning that there is a slight "predictability" or "forecastabililty" from one day to the next. The Hurst exponent, Fast Fourier Transform, and entropy studies of the indices seem to support the contention, also, (the entropy is too low, implying that the increments are not as random as a random walk would suggest.) The Hurst exponent, in addition, seems to indicate that there is a four year "cyclic" phenomena in the indices-which could be interpreted as the signature of a chaotic mechanism, possibly a strange attractor, (but there could be structural reasons, too.) There are graphs of the Hurst exponent for the NYSE at: http://www.johncon.com/john/correspondence/980807151309.11811.html http://www.johncon.com/john/correspondence/980807152940.11914.html http://www.johncon.com/john/correspondence/980807154817.12009.html But as a first order approximation, a random walk fractal seems adequate-at least as a conceptual description from a stochastic point of view-and the mathematics of the statistics is simple, (ie., "bubbles" in the stock market follow a 1 / sqrt (t) frequency distribution, etc.) 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 18:52:52 PST 1999 $Id: 990205113415.1038.html,v 1.0 2001/11/17 23:05:50 conover Exp $