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<DIV><FONT color=#000000 size=2>I received one response to my post asking about
the 13 pt scale on a copy of an original Gann Chart. Here is my response. I
would like to pursue these basic lines of thought further if anyone is
interested. </FONT></DIV>
<DIV><FONT color=#000000 size=2></FONT> </DIV>
<DIV><FONT color=#000000 size=2> Ken,<BR>The 13 pt scale is 13 pts per
1/8" on the price of cotton. e.g. from $.3640<BR>to $3692 occupies
1/2" on the price axis.<BR>I asked several people who have studied Gann and
they all draw a blank. My<BR>main question for Baumring students is what do they
know about simple<BR>scaling of charts. It seems to me that is
fundamental.<BR><BR>I haven't studied astrology in years.<BR><BR>My recent
studies are more in the area of probability and statistical<BR>analysis of time
series. A subset of this is digital signal processing.<BR>Because of the
incomensurable nature of the planetary cycles (ie non whole<BR>number
relationship) a superposition of cylcles can produce the appearance<BR>of a
random walk in an alleged resultant composite economic time series<BR>such
as the DJIA. In other words any outcome is explainable by chance.
With<BR>constantly varying phase, angular velocity, and amplitude it is hopeless
to<BR>try and resolve effects into causes. Therefore, I no longer try to do so.
At<BR>the same time I try to keep an open mind...</FONT></DIV>
<DIV><FONT color=#000000 size=2></FONT> </DIV>
<DIV><FONT color=#000000 size=2>George</FONT></DIV>
<DIV><FONT color=#000000 size=2></FONT> </DIV>
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<DIV><FONT color=#000000 size=2></FONT> </DIV>
<DIV><FONT color=#000000 size=2>
<DIV><FONT size=2>With regard to this price-time vector, I just happen to be
reading Benoit Mandelbrot's Fractals and Scaling in Finance. In chapter 6 'M'
says: "... financial charts...show the abscissa as the axis of time
and the ordinate as the axis of price. The scale of each coordinate can be
changed freely with no regard to the other. This freedom does not prevent a
distance from being defined along the coordinate axes. But for all other
directions, the Pythagorean definition,</FONT></DIV>
<DIV><FONT size=2></FONT><FONT color=#000000
size=2> </FONT></DIV>
<DIV><FONT color=#000000 size=2>
distance= square root of (time squared + price
squared) { d = (T^2 + P^2)^.5
}</FONT></DIV>
<DIV><FONT color=#000000 size=2>
</FONT></DIV>
<DIV><STRONG><U><FONT size=2>makes no sense whatsoever.</U></STRONG> It follows
immediately that circles are not defined... Squares are not defined, since -
even when their sides are meant to be parallel to the axes- there is
<STRONG><U>no sense in saying that time increments = price
increment.</U></STRONG> </FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>There is a different linear operation that applies different
reduction ratios along the time and price axes. It generalizes, and
Leonard Euler called it an affinity. ... It follows that for graphs of functions
in time, like price records, the relevant comparison of price charts over
different time spans involves the scaling notion of self-affinity. Self-affinity
is more complicated and by far less familiar than
self-similarity..."</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>In all honesty I have only a hazy notion of self-similarity
and hope that some RT may provide the appropriate explanation of self-affininty
and self-similarity with examples for a layman.</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>My own simple example of scaling behavior is as follows: If an
animal builds a square (or equilateral triangle) shaped dwelling one meter on a
side and then dilates to say 5 meters on a side the floor (or roof area) expands
as a 2nd power of the ratio (5:1) giving 5^2=25 as the scaling behavior. The
"alpha" or powering in this case is 2. We are talking nonlinear
here or parabolic expansion of area (A) with side (s): A=s^2 Given a side
(s) I can predict the area (A) because I know the scaling behavior of the animal
and I assume that it remains stationary in a statistical sense for the
forseeable future.</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>Although on thin ice here, as best I can tell <FONT
size=2>Mandelbrot maintains </FONT>that the markets are a scaling phenomena over
time. They expand out in some powering of time say 1.5. This is similar to
Einstein's brownian motion in which molecules on average diffuse proportional to
the 1/2 power of time. Kepler's law has the periods of the planet's scaling out
at 1.5 power of the radius (t^2=r^3). M also mentions Paretos law of incomes.
Again, my crude understanding is that the relative frequency (ie probability) of
someone with four times the median income is not 1/4 the probability of the mean
earner but one over four to some power say 3 for example. Prob =
1/4^3</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>Another point made by M is that the statistical distributions
of price change (or rates of return) are not Gaussian. The relative
frequency of large price changes is considerablely greater than the the so
called "normal" distribution. (ie the distribution of price change has
fatter tails). My example is men's heights. Say the standard deviation of men's
heights is 6" around 5'-10" mean. We expect 99.7% of men to fall
within a range up to 7'-4" (5'10" + 3 standard deviations). We don't
expect 2 % of men to be 11 feet tall! but in the market we do.(This is the tail
of the distribution)</FONT></DIV>
<DIV><FONT size=2>Also market prices exhibit a clustering that M calls the
"Joseph effect". The latter term comes from the Bible story of 7 good
years followed by 7 lean years. The 7 may not be important but the clustering
effect is. This clustering is what appears on a chart as a trend.</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>I hope the above provides some ideas.</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>One question that has arisen in the course of my time series
studies is what effect the simple act of pulling prices out of their time slot,
rearranging them into ascending order, and plotting the histogram ("bell
shaped curve") has on the information content of time series such as daily
closing prices? Are we distorting the process from the get go? I mean, try and
guess how many ways one can scramble the misspelled word permutaion? Answer
10!=3,628,800. Ditto for the last 10 days closing prices of the Dow. Now with
3,628,800 realizations possible for the scambling of the last 10 days closing
prices what is the justification for picking one (ascending order) and applying
all these statistical tools to it? Just because they are the only tools in our
toolbox? </FONT></DIV>
<DIV> </DIV>
<DIV><FONT color=#000000 size=2>George</FONT></DIV>
<DIV><FONT color=#000000 size=2> </FONT></DIV></FONT></DIV></BODY></HTML>
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From: "Gitanshu Buch" <OnWingsOfEagles@xxxxxxxxxxxxx>
To: <realtraders@xxxxxxxxxxxxxxx>
Subject: [RT] MKT: OEX / HV part 2
Date: Sun, 9 Jan 2000 16:53:00 -0500
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Status:
It is time to expect a contraction in price volatility in the next
week...although the VIX started doing it on Thursday.
Comments on chart.
Gitanshu
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