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

Subject: Re: Time Varying Dimensions of Time Series

Date: 10 Jul 1999 02:32:00 -0000

Hi Konstantinos. You might want to look back a few years into applications of the logistic (eg., discreet time parabolic,) function which is known to exhibit chaotic phenomena. A series of interacting logistic functions, or S-Curves, was suggested by William S. Jevons, (as cited Alfred Kleinknecht,) in 1884-but there were earlier works, too. R. Ayres extended the concept, and so did the Russian economist N. D. Kondratieff in 1926. Schumpeter made contributions, also. As far as I know, the concept has fallen into disfavor, and is no longer considered mainstream contemporary economics, but FYI. A reasonable modern reference is: "Predictions", Theodore Modis, Simon & Schuster, New York, New York, 1992. For chaotic time series, the science has changed in the past decade. A truly excellent reference and tautology is: "Chaos and Fractals: New Frontiers of Science", Heinz-Otto Peitgen and Hartmut Jurgens and Dietmar Saupe, Springer-Verlag, New York, New York, 1992. where it is proposed to make a parametric plot of the time series, ie., shift the time series by one time unit, and plot x,y. If a geometric pattern emerges, then the variable values can be measured in the chaotic time series. If the pattern is a "splatter", then the time series is stochastic. John Konstantinos Euripides Vorloou writes: > I think his last paper on this is in Physica A: > > Benoit B. Mandelbrot, Renormalization and fixed points in finance, since 1962, > Physica A: Statistical Mechanics And Its Applications (263)1-4 (1999) pp. 477-487 > > That's where the Sci. Am. article comes from... > > I've read this article. I was thinking though of the time series being generated > as the result of the interaction between several chaotic systems and not by the > changes occuring > in one only system. Something like a mixed chaotic process. > > Is there anything relevant out there ? Anywhere ..... > > conover@rahul.net wrote: > > > David Lloyd-Jones writes: > > > > > > Konstantinos Euripides Vorloou <K.E.Vorloou@durham.ac.uk> asks: > > > > > > > > Is there any literature or ideas on the way (this way could be > > > > deterministic or stochastic) dimensions of (chaotic) time > > > > series may change within their histories ? > > > > > > . > > . > > . > > > > > > Mandelbrot fired off these cannons, and then went on to other things, and > > > has only returned to economics a little bit recently. In a letter to the > > > editors of Scientific American dated April or May of this year he gave the > > > few revisions he felt like making to his 1963-65 positions. Fama's first > > > paper above is a review which neither supports nor opposes Mandelbrot's > > > manifesto. The second one calls for more empirical research on Mandelbrot's > > > "hypothesis," a word this latter would not have used to characterise his > > > dicta. > > > > > > > The latest Mandelbrot citation is "A Multifractal Walk Down Wall > > Street," Benoit B. Mandelbrot, Scientific American, February 1999, > > pp. 70-73. > > > > John > > > > -- > > > > John Conover, john@email.johncon.com, http://www.johncon.com/ > > -- > > > "Research is to see what everybody else sees, > and to think what nobody else has thought." > > Albert Szent-Gyorgy > > ------------------------------------------------------------------------- > Konstantinos E. Vorloou | Tel: +44 (0)191 374 1821 > Department of Economics & Finance | Fax: +44 (0)191 374 7289 > University of Durham, | email: K.E.Vorloou@durham.ac.uk > 23/26 Old Elvet, | or : vorlow@rocketmail.com > Durham DH1 3HY, | or : Vorlow@bigfoot.com > UK. | Express: 20595534@pager.mirabilis.com > | ICQ number: 20595534 > http://www.durham.ac.uk/Economics | http://www.durham.ac.uk/~dec3kev > ------------------------------------------------------------------------- > > -- John Conover, john@email.johncon.com, http://www.johncon.com/

Copyright © 1999 John Conover, john@email.johncon.com. All Rights Reserved. Last modified: Sun Nov 14 00:01:35 PST 1999 $Id: 990709193213.17992.html,v 1.0 2002/02/12 19:54:06 conover Exp $