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 20:43:00 -0000
BTW, Jeff, if you run tsdeterministic on the time sampled DJIA, (say,
take every 1020'th sample, i.e., about one every 4 years-maybe using
the tssample program,) you will find some kind of geometrical function
that has a phase portrait that repeats, (sort of,) every modulus 4,
minus 1, years. You have to look very hard for it, but its there.
Whether it is the characteristic of a NDLS system, (many consider it
adaquate evidience that it is, and many don't,) or the result of
structural issues, (many don't, and many think it is-and offer a
variety of inductively rational reasons,) is debatable.
In fact, we will never know, since NDLS systems are globally stable,
and everywhere, locally, unstable-meaning that they tend to phase lock
on structural phenomena that are insignificant, with significant
results; any predictability in such systems decays exponentially into
the future, (like the weather, for example-where in the temperate
regions, just saying that the weather tomorrow will be like to day
carries a 70% probability of being right; about the same as the
forecasts produced by the best physical models, on average.)
However, you can exploit the modulus 4 minus 1 year phenomena. If you
struggle through the math, and run good metrics, you will run about a
65% prediction accuracy. So, you would bet 2P - 1 = 1.3 - 1 = 30% on
the prediction, (you could do no better in the long run-that is
optimal,) and your gain would be about 1.04676, or about 5% every 4
years, or a little over a percent a year.
With the DJIA running about 10% year, average over the 20'th century,
it would be a substantial gain over an investing lifetime of 60 years,
or so; about 2X.
John
John Conover writes:
>
> 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/