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