From: John Conover <john@email.johncon.com>
Subject: Re: A year ago today, the NASDAQ was at an all time high
Date: 13 Mar 2001 20:16:17 -0000
Hi Jeff. If you let your random number generator go long enough,
tsdeterministic will show that the pseudo-random sequence repeats.
For a 32 bit machine, that will be a sequence of a minimum of 4
billion numbers before the sequence repeats for another 4 billion
numbers, (most random number generators use two integers, for a
sequence free interval of 1.8e19, which is near Heisenburg's
uncertainty of e22, which is practical enough for anything in the real
world.)
The parametric geometric figure you get from tsdeterministic will not
be a parabola, (except for the logistic function, which is also known
as the discreet time parabolic function, because its parametric
geometrical map is a parabola-which you showed.) The logistic function
is but one of a family of discreet time functions-each of which has a
characteristic parametric geometric plot-including all pseudo-random
number generators.
The reason you see a straight line when running tsdeterministic on the
the DJIA time series is that a parametric geometrical map of an
exponential is a straight line.
The way you get from one time point, to the next, is to multiply the
point by a constant, (1.0003... in the case of the DJIA.)
That's a formula for compound interest, which has an exponential
characteristic.
Tsinvest does the same thing. If (v(n) - v(n - 1)) / v (n - 1) is
constant, then it is an exponential. The average, avg, and root mean
square, rms, of these can be used:
P = (avg/rms + 1)/2
G = (1+rms)^P * (1-rms)^(1-P)
to do the same thing. (If rms = avg, then P = 1, and G = 1 + rms.)
The slope of the parametric geometric plot is G.
So, you have just verified the validity of the methods used in
tsinvest, using non-linear dynamical system, (NLDS, e.g., chaos,)
methods, (a state-phase portrait, a la Poincare, to be exact; which is
kind of trick-the parametric geometric map, or state-phase portrait,
is not a function of time.)
John
Jeff Haferman writes:
> John Conover wrote:
> >
> >BTW, while you are on the Utilities page, pick up the tsdlogistic
> >program, too. Do "tsdlogistic -a 4 -b -4 1000 > XXX", and plot
> >XXX. Looks like a stock's price-very noisy. Then do "tsdeterministic
> >XXX > YYY", and plot YYY. The marvels of deterministic systems-a
> >perfect parabola. The point being, some noisy systems are
> >deterministic, and predictable-others are not. Equity markets fall
> >into the latter case.
> >
>
> I've seen this explained in a book that I know is on my shelves,
> but I can't seem to recall which book. So, I need to ask
> a few questions:
> Yes, I get a parabola when I follow the instructions that
> John outlined.
>
> But, I don't get a parabola when I feed tsdeterministic
> uniformally distributed psuedo-random numbers, eg
>
> SEED = 12357
> DO I=1,N
> SEED = 2045*SEED+1
> SEED = SEED-(SEED/1048576)*1048576
> X = REAL(SEED+1)/1048577.0
> ENDDO
>
> Though this is deterministic, right?
>
> Furthermore, what about the case
> DO I=1,N
> X = I
> ENDDO
>
> I don't get a parabola when I feed this last case to
> tsdeterministic. (I get a 45 degree line, but that's
> also the sort of thing I get when I feed daily price
> data to tsdeterministic).
>
> What am I missing here?
>
> Jeff
--
John Conover, john@email.johncon.com, http://www.johncon.com/