From: John Conover <john@email.johncon.com>
Subject: Re: rms of indices
Date: 3 Jan 2001 08:48:04 -0000
And, then if you are a real glutton for punishment, you can write a
program that does a point-by-point reconstruction of the indice using
the formula:
G = (1 + rms)^P * (1 - rms)^(1 - P)
for each P and rms in both files.
You will find that the indice can be reconstructed, (differing only by
a scaling constant,) from its statistics-a validation of the model
used.
John
BTW, there are a lot of tricks that can be used from the
http://www.johncon.com/ntropix/utilities.html page. The tsgainwindow
does about the same thing, but a geometic progression has to be done
on the output.
John Conover writes:
> BTW, another interesting thing to do is:
>
> tsshannonwindow -w 100 -a -b -c -d -e -f -g -h data_file
>
> which calculates the Shannon entropy, using different methods. Vary
> the -w argument.
>
> The first thing one notices is that the Shannon entropy is fractal,
> (unless the -w argument is set to many thousands-consistent with the
> tsshannoneffective program,) and all the methods give values that
> are very close to the theoretical value:
>
> P = ((avg / rms) + 1) / 2
>
> even though some of the methods don't measure the avg or rms at all,
> (for example, some just count the number of ups, and downs, and
> compute the entropy from ups / (downs + ups) in the time interval
> defined by the -w argument.) Others assume that the absolute value of
> the movements are the same as the rms.
>
> Its kind of an interesting exercise.
>
> John
>
> BTW, the manual page for the tsshannonwindow program is at:
> http://www.johncon.com/ndustrix/archive/utilities/tsshannonwindow.txt, and the
> output is a standard Unix tab delimited file. So, use "cut -f1,2" and
> "cut -f1,3" and so on to get different files of the different methods
> of calculating the Shannon probability. Its kind of interesting to
> make a plot of them overlayed. The gist of it is that stocks increase
> in value, (or decrease,) more based on the ratio of the number of up
> movements to down movements in an interval than by the magnitude of
> the movements in an interval. Kind of counter intuitive, (and a good
> empirical statement of the fractal nature of such things.)
>
> John Conover writes:
> > Just as kind of an FYI, Blake LeBaron,
> > (http://www.ssc.wisc.edu/~blebaron/,) one of the NLDS, (chaos,)
> > theorist pointed out in 1991, that for some reason, market crashes are
> > always preceded by an increase in the root mean square of the daily
> > marginal returns of the indices. (Which is vary characteristic of
> > bifurcations in NLDSs.)
> >
> > If you use the tsrmswindow program, (from
> > http://www.johncon.com/ntropix/utilities.html,) on the historical
> > database of the DJIA, S&P500, and NASDAQ, it seems to be true. For
> > example:
> >
> > tsfraction data_file | tsrmswindow -w 100
> >
> > where data_file is the time series for the NASDAQ, will make a plot
> > file that shows that for several years, the rms values have been
> > running about 3X their average value-averaged since 1971. A like
> > scenario happened in the late 20's to the DJIA and S&P. Likewise for
> > the other crashes and crash'ets of the 20'th century.
> >
> > John
> >
> > BTW, as nearly as I can tell, the US equity market has degenerated
> > enough such that 5-10% of the US's net wealth has went up in smoke.
> > About 3-5 trillion bucks have been lost, (depending on who is doing
> > the counting,) and the US net wealth is estimated at about 50 trillion
> > bucks-about a forth to half of the world's net wealth, (Re: the US
> > FED-I have no idea how they measure that; what is the value of the
> > nuclear weapons arsenal? How is it depreciated?) Its a fairly sizable
> > chunk of the world's net wealth.
> >
--
John Conover, john@email.johncon.com, http://www.johncon.com/