From: John Conover <john@email.johncon.com>

Subject: Re: forwarded message from John Conover

Date: Tue, 29 Oct 1996 02:38:42 -0800

And, in case you are still curious, one can say that the stock market indices are beyond fractal, (which is the simplest kind of analysis,) and say it is a non-linear dynamical system, or in the lay vernacular, a chaotic system. If you do a chaotic analysis[1], and get the Lyapunov exponent that describes the horizon of predictability of the indices, it provides yet a 4th method that is in agreement. This is the method that I used in February to forecast the June correction. It too says that a correction is likely, (but not guaranteed,) in October/November. And, in case you are further interested, there is another mean reverting phenomena every 2/3 of a year, but it is milder than the 5.5 year scenario. And, additionally, at 4.2 years, the market seems to replicate itself, ie., if it is good now, it will be good in 4.2 years. Likewise for bear markets. At least on the average of a century of daily returns of the DJIA. Like I say, no one knows why-but there is substantial evidence that it is a chaotic phenomena. But no one has been able to model it, nor exploit it successfully. But a lot of math folks are being conservative, and running from it, (ie., take the money and run.) FWIW ... John John Conover writes: > In case you are curious, the reason that folks like Garzarelli are > making these kind of predictions is that if you take the range of > values of the stock market indices over a time interval, and divide it > by the standard deviation of the stock market indices over that time > interval, and do that for all values of time intervals, you can make a > Hurst Coefficient plot[1][2]. The program tshurst.c (from the usual > places,) will do that for you. Be advised that it is a problem in > combinatorics, and you will have to run it on a century of the daily > returns of the DJIA, or a half a century of the S&P. It will take > several weeks of processing on a Pentium 90, (the data sets are > moderate, there is no file I/O issues-it is a straight NP problem.) > > What you will find is that, for reasons that are not understood, the > markets are mean reverting on a cyclic phenomena of about 5.5 years. > That means that if you look back 5.5 years, whatever the market was > 5.5 years ago, the market now will be the opposite, on the > average. The rather impressive growth in the values represented by the > equity market indices over the last 18 months, or so, was created by > the late October 1987 "crash," according to this concept. The "crash" > was followed by a period of equally impressive market growth, so that > means, that on the average, we should be entering a down cycle. > > If you plot the 26 thousand day history of the DJIA, and go through > it, day by day, you will find that the evidence for such a proposition > is VERY strong-so strong it can not be written off as a fugitive of > statistical law. The prevailing concept is that it is created by a > "chaotic phenomena," (presumably like weather patterns.) > Unfortunately, there have been many attempts to explain it, but it has > defied analysis, from some very formidable attempts. But it is there. > > She got the 15 to 25 percent number by averaging the fair market value > of many stocks by computing a stock's fair market value from the > stock's volatility, first derivative, and absolute value[3], over the > history of the DJIA, (you can use the programs tsrms.c, tsavg.c, and > tsmath.c to do this.) This value is currently about 20% overvalued. It > typically runs about 5%. > > See the references for different methodologies of arriving at the same > conclusion. [1] references a method of auto-correlation, which should > be computationally efficient. Fourier analysis has also been used. The > results of the different methods is, approximately, the same. (Rather > astonishing when you think about it-that the power frequency spectrum > of the DJIA, and the range, ie., max - min, of the time series, as a > function of incremental time-which is proportional to the square root > of time-all produce the same conclusion, which agrees with correlation > techniques. But no one can find out why.) > > John > > [1] "Nonlinear Time Series, Complexity Theory, and Finance," William > A. Brock, Department of Economics, The University of Wisconsin, Pedro > J. F. de Lima, Department of Economics, The Johns Hopkins University, > reprinted in "Handbook of Statistics, Volume 14: Statistical Methods > in Finance, G. Maddala, C. Rao, eds., North Holland, New York, New > York. > > [2] "Chaos and Order in the Capital Markets: A New View of Cycles, > Prices, and Market Volatility," Edgar E. Peters, John Wiley & Sons, > Inc., New York, New York, 1994. > > [3] Let F be the root mean square value of the normalized increments > of the stock's time series, and the absolute value of the time > derivative of the stock's price time series is the fluctuations in the > stocks price, ie., at any instant, if V is the stock's price, then FV > will be the fluctuation in price, which is the derivative, D, or, V = > D / F. In other words, the fair market value of the stock, in relation > to the normalized increments of the stock's value, will be the > derivative of the stock's price, divided by the root mean square of > the normalized increments of the stock's price. > -- John Conover, john@email.johncon.com, http://www.johncon.com/

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