# Re: rms of indices

From: John Conover <john@email.johncon.com>
Subject: Re: rms of indices
Date: 3 Jan 2001 09:12:03 -0000

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This is why the second paragraph of the quality assurance page,
http://www.johncon.com/ntropix/QA.html, works.

Note that all that was done was to extract the analytical data from a
set of stocks, (three numbers for each stock,) and use those numbers
in an inverse function, (simulation,) to reconstruct the original
data-and then analyze the reconstructed data, and compare the original
analytical data with the reconstructed analytical data.

John

John Conover writes:
> 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/

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