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/

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