From: John Conover <john@email.johncon.com>
Subject: Re: forwarded message from John Conover
Date: Tue, 29 Oct 1996 02:12:33 -0800
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 writes:
>
> Predictions like the attached are interesting. If you look at the
> statistics of such prognistications, 52% of the time they will be
> correct, 48% incorrect. (Likewise, saying that the market value will
> increase in November would carry about the same statistics-you would
> run about the same chance of being correct, also.)
>
--
John Conover, john@email.johncon.com, http://www.johncon.com/