From: John Conover <john@email.johncon.com>
Subject: Re: A year ago today, the NASDAQ was at an all time high
Date: 14 Mar 2001 02:17:17 -0000
Notice the statement:
BTW, note the paradigm of the FED when using adaptive control
techniques. They tend to use NLDS and stochastic methodologies
interchangeably-which, and when, depends on practical issues.
If you look at the way the logistic process works, we take the
previous value in the series, and do something to it to get the next
value.
If you look at the way the tsinvest program works, it does much the
same thing.
For example, I could use the tsfraction program on a time series, pipe
its output to the tsavg and tsrms programs, and get the same data that
is in the internal data structures in tsinvest, (the avg and rms of
the time series, for example, and then compute P = (avg/rms + 1) / 2,
then G, and so on.)
I could also take the output of the tsfraction program, and modify it,
(subtract avg, for example, using tsmath -s,) and then pipe that
output into tsunfraction, which would reassemble the time series, with
avg = zero.
The process of tsunfraction is very similar to producing the logistic
process. It takes the last value, multiplies it by the current value
to get the next value. The tsinvest program just does the opposite-it
disassembles things, in an attempt to determine the parameters,
assuming a first order non-linearity. (Note the assumption-an equity
price does *_NOT_* have random walk walk characteristics; a random
walk is an additive process; tsinvest assumes it is multiplicative,
and, therefore, a non-linear process.)
Note the paradigm: an equity price is produced by a complex system,
perhaps even an NLDS; I will truncate the higher order terms, using
only the first non-linear term, (a la approximation by truncating a
Taylor polynomial,) and model the higher order terms as a stochastic
process, since I can not measure the parameters of the NLDS because of
Ljapunov issues. Since, if it is an NLDS, I might have some short term
predictability, I will model that as persistence-increasing the
fractal dimension-since the future will depend, slightly, on the past,
(and that is what the -d5 option does in tsinvest.)
Whether equity prices have NLDS, or stochastic characteristics with
persistence, is an intellectual issue, and not a practical one, (even
if such a determination was possible, which it isn't; although most
folks-me included-have a religious belief that it is NLDS.)
This is what Rucker's book is all about.
Note that many things in the world are that way-white stellar noise,
(the best noise generator available,) was created by a deterministic
system; a mechanistic process.
John
John Conover writes:
>
> Its funny you should mention that-I got the e-mail as I was writing
> about the complexity characteristics of the logistic equation. Peters
> has one of the best presentations of the Ljapunov exponent I've
> seen. (Both of his books are excellent and practical for the equity
> investor, BTW.)
>
> If one tries to determine a and b in the logistic equation, the error
> of prediction, although quite small to start with, grows
> exponentially. The constant in the exponential error growth is the
> Ljapunov exponent.
>
> Its an important concept these days. The idea that things like
> recessions could be averted through manipulation of monetary policy,
> (an idea in vogue in the 70's,) and then fiscal policy, (the vogue
> idea in economics in the 80's,) has largely been abandoned.
>
> The idea now, (its the way the FED does things-and the FED is the
> largest consumer of mathematical programming software in the world
> today,) is to continually measure the parameters-almost real time,
> (like a and b in the logistic equation-but they have hundreds or
> thousands of such parameters,) and then tweek things dynamically, very
> quickly to avoid the predictive implications of Ljapunov exponent, and
> exercise some control over the economy.
>
> Its a new field in complexity theory called "adaptive control," and it
> is in its infancy, (the people at the FED published a paper on it a
> few years ago-in the list of authors was one Alan Greenspan; it is
> most used to mitigate inflation, which is the most evil demon that a
> finance minister can face.)
>
> Adaptive control is domain of the Santa Fe Institute, (among others,)
> and Stephanie Forrest, (formerly of SFI, now at the University of New
> Mexico,) is one of the foremost researchers. (She did the genetic
> algorithm programming as an graduate student for Robert Axelrod's
> famous iterated prisoner's dilemma experiments in political science,
> too-which changed the paradigm of the profession, and gave substantial
> evidence that John Nash's game-theoretic solutions were correct; of
> interest, note how the computer abstraction played a part in
> mathematical proof!.)
>
> John
>
> BTW, note the paradigm of the FED when using adaptive control
> techniques. They tend to use NLDS and stochastic methodologies
> interchangeably-which, and when, depends on practical issues.
>
> Jeff Haferman writes:
> > BTW,
> > You may be interested to know that Edgar Peters has a new
> > book out:
> > "Complexity, Risk, and Financial Markets", by Edgar Peters,
> > John Wiley and Sons, 2001, ISBN 0-471-39981-7, (paperback).
> > This differs from Peters earlier books ("Chaos and Order
> > in the Capital Markets..." and "Fractal Market Anaylsis")
> > in that there aren't really any equations in the entire book
> > (there may be one or two fairly simple equations). Another
> > book by Peters (1999 "Patterns in the Dark") drew some
> > criticism on the reviews at Amazon that it was "dumbed down"
> > to "reach a broader audience". I haven't read "Patterns
> > in the Dark", but I have read "Complexity, Risk, and
> > Financial Markets" and it is a good, thought-provoking read.
> > The other nice thing is that it is relatively cheap ($16 or so).
> > I like mathematically rigorous writing, but this was a book
> > was a nice change of pace.
> > Jeff
> >
> >
> > John Conover wrote:
> > >
> > >While we are on the subject of good books about things fractal and
> > >chaos, here are a few of my favorites:
> > >
> > > "Mind Tools", by the logician Rudy Rucker, (more noted as a
> > > science fiction author, and a world renowned mathematician-he
> > > personally worked with Kurt Goedel,) Houghton Mifflin Company,
> > > Boston, Massachusetts, 1993, ISBN 0-395-46810-8, (paperback.)
> > > Rucker is at the forefront of science in the 21'st century,
> > > (looking after the formal issues,) and the book is about
> > > complexity, and how information theory, math, logic, and
> > > randomness are all tied together. It is non-technical, but that
> > > doesn't mean the reader does not have to think. If I were king,
> > > all high school diplomas would be issued only after a student had
> > > demonstrated competency with the content of this book.
> > >
> > > The Stewart book, (mentioned previously,) "Does God Play Dice?:
> > > The Mathematics of Chaos", Ian Stewart, Blackwell Publishers,
> > > Cambridge, Massachusetts, 1992, ISBN 1-55786-106-4. It is very
> > > heartening that a mathematician of the stature of Stewart would
> > > set down and write a book about randomness for the lay
> > > person. This book addresses predictability, randomness, and
> > > entropy, and how they are related, (and how they are not.) Note
> > > that we really don't know what the word random means. (Could you
> > > explain it?)
> > >
> > > "The Jungles of Randomness: A Mathematical Safari", Ivars
> > > Peterson, John Wiley & Sons, New York, New York, 1998, ISBN
> > > 0-471-16449-6, a good introductory book on simple fractals, with
> > > real-life examples, and how fractals, chance, and randomness work.
> > > Perhaps available now in paperback.
> > >
> > > "What is Random?: Chance and Order in Mathematics and Life",
> > > Edward J. Beltrami, Springer-Verlag, New York, New York, 1999,
> > > ISBN 0-387-98737-1, (I don't know about paperback.) A bit more
> > > technical and formal approach to randomness, and how it is tied
> > > into information theory.
> > >
> > > John
> > >
--
John Conover, john@email.johncon.com, http://www.johncon.com/