# Re: rms of indices

From: John Conover <john@email.johncon.com>
Subject: Re: rms of indices
Date: 3 Jan 2001 08:25:51 -0000

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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/

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