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Have to disagree. What you want is not necessarily a scale-independent approach, but a construction that provides support and resistance and interacts correctly with line studies, etc.. There are many examples that show howprices often tend to follow the circular arc, as shown on most of the charts in my post, and not just hit it at a point or two. Imagine an elliptical arc superimposed on those charts and see if that provides the same information. Certainly, since it slopes upward at a sharper angle it will tend to cut through s/r areas, rather than provide s/r. So, contrary to your conclusion, such charts suggest to me the need for circular arcs. Unfortunately, there appears to be no way around the scaling issue, but if one, as yousuggest, studies the intention of the arcs and the way they were developedthen it is not clear that there is anyway around using circular arcs when appropriate. Be that as it may, as I said before elliptical arcs might be equal or superior to circular arcs. However, if there is a case to be madefor elliptical arcs then it will have to be done over time with a variety of markets and time frames, which to the best of my knowledge has not been done. This is not a theoretical exercise, but one of establishing whether or not a correlation exists, which will take considerable effort to prove or disprove. At this point in time, we have a long history associated with circular arcs and one should reject that history with caution.
Bill
----- Original Message -----
From: AR.Holzwarth@xxxx
To: amibroker@xxxxxxxxxxxxxxx
Sent: Tuesday, August 14, 2001 8:36 AM
Subject: Re: [amibroker] Cycles
"...Note that the points where the Arcs cross the price data will vary depending on the scaling of the chart, because the Arcs are drawn so they arecircular relative to the chart paper or computer screen. ..."
Wavemechanic,
your above mentioned citation from "Windows on Wallstreet" could not say it better. There you have the problem explained exactly as it stands. This should convince you that in fact you want scaling-independent crossing points. You get proper scaling-independent crossing points when you use the definition that Dimitris has given for the arc. This is valid despite the (inevitable by the way) fact that upon rescaling of one axis you get "illegal" circles, as you like to call ellipses. The term "illegal circle" for an ellipse is not very common in mathematics though.
Rather than doing things just "mechanically", it is important to understand what was the original intention of the Fibonacci "circles", or "ellipses" as they should have better called them.
Regards
Alf
----- Original Message -----
From: wavemechanic
To: amibroker@xxxxxxxxxxxxxxx
Sent: Tuesday, August 14, 2001 12:36 AM
Subject: Re: [amibroker] Cycles
Dimitris:
(I assume that Cycles = Circles)
Well not quite the "last lines." Your algebra and geometry in this andprevious notes are flawless, and you clearly have conquered the equation of a circle without doing harm to the work of the ancients. But that was never the question.
What you have said about programming and displaying a circle is exactlyright. However, it is essential to understand a tool and how it is used before programming it. As you have discussed and shown, if you plot relative to the X & Y axis you usually get an ellipse. This, however, is not whatyou want, which is the reason that software with canned Fibonacci arcs plot relative to screen coordinates so that a circle is displayed. Why do yousuppose that virtually all charting programs plot circular arcs at all magnifications and time periods? This is not a matter of mathematics or programming.
The problem with not plotting relative to the screen reflects the dual purpose that arcs are used for. The first function is to identify support and resistance and the second is to interact properly with line studies, ineach case providing price and time projections. Both of these have to be effected by plotting relative to screen coordinates. Hopefully, a picture is worth a thousand words. The attached schematic clearly indicates that acircle on the screen is not the same as an ellipse with respect to either of these functions. In this simple example, it is clear that the circular arc has provided resistance as it should. Also, although I did not draw itin, it is easy to imagine a line study (e.g., a tangential line) producingvery different projections for the circle and ellipse. As I said in my Circular Fibonacci Arc note, one can use any shape on the screen that one wants. However, based on experience circular is the way to go, and in this business, correlations are all that we have.
Remember that these techniques were used back when everything was plotted by hand. It is up to commercial programmers to duplicate these conditions. Unless this is done one is dealing with an entirely different, untested "animal" that may or may not be better. So far, this is not the route followed by software suppliers. Of course, the individual can always choose a different path and customize the arcs, especially with currently available programs, such as AmiBroker, that are relatively easy to program.
The internet is loaded with discussions and examples of Fibonacci Arcs with and without line studies. If you are interested in this subject, it would be worth your time to read about it, as well as note how other charting programs handle the circular vs elliptical arc issue. To speed the process up for you and others, I copied some charts from a variety of sites. Superimpose on these images an elliptical arc and see whether it works as well as circular with respect to support/resistance and interaction with line studies. Perhaps this exercise will result in improved arc formulation, use, and interpretation.
Hope this helped you.
Bill
Market Analyst II
Windows on Wallstreet
A common technique is to display both Fibonacci Arcs and Fibonacci Fan Lines and to anticipate support/resistance at the points where the Fibonacci studies cross. Note that the points where the Arcs cross the price data will vary depending on the scaling of the chart, because the Arcs are drawn so they are circular relative to the chart paper or computer screen.The following British Pound chart illustrates how the arcs can provide support andresistance (points "A," "B," and "C").
Trendsoft
Arcs combine time and price to display expected containment of price action over time. Circles are used to identify the significant high and low used for these indicators. Note how prices found support, after the significant high at the outer arc.
Many analysts use arcs and fan lines together expecting significant
support or resistance to occur where these lines cross.
Stockhouse
----- Original Message -----
From: Dimitris Tsokakis
To: amibroker@xxxxxxxxxxxxxxx
Sent: Monday, August 13, 2001 3:19 PM
Subject: [amibroker] Cycles
Dear Bill,
Besides what analysts may say through you, here is the last lines
on the subject.
Open ANY textbook to read the equation of a circle.
The happy condition is that we all agree on that the last 2500 years
(x-x0)^2+(y-y0)^2=R^2
where x0, y0 the coordinates of the center and R the radius.
This, in order to be graphed, must be solved for y and come in the
form y=f(x).
The solution is
y=y0+sqrt(R^2-(x-x0)^2
y=y0-sqrt(R^2-(x-x0)^2
(ask the nearest Math Department if you doubt for the solution)
For a day graph we use here
x=cum(1);
(this is the independent variable x=1, 2, 3, etc)
and the code to graph a circle, centered at (380,0) with R=20
is
/*CYCLE*/
x0=380;
y0=0;
R=20;
x=cum(1);
y1=y0+sqrt(R^2-(x-x0)^2);
y2=y0-sqrt(R^2-(x-x0)^2);
graph0=y1;
graph1=y2;
graph1barcolor=graph0barcolor=2;
The result is graphed t w i c e in attached gif.
Exactly the same cycle.
What you see is a cycle, has the math properties of a cycle
and obeys the common for the whole world equation of a
cycle.
With this you may solve a lot of problems, especially if you
are interested for the points this circle cuts other lines,
because it is the equation of the cycle
This note in addition to #3825 Re:Angles is covering the
subject sufficiently enough.
If you mind for the visual part, I have nothing more to add.
Friendly yours
Dimitris Tsokakis
Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.
Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.
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<DIV><STRONG><FONT size=2>Alf:</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>Have to disagree. What you want is not
necessarily a scale-independent approach, but a construction that provides
support and resistance and interacts correctly with line studies, etc..
There are many examples that show how prices often tend to follow the circular
arc, as shown on most of the charts in my post, and not just hit it at a point
or two. Imagine an elliptical arc superimposed on those charts and see if
that provides the same information. Certainly, since it slopes upwardat a
sharper angle it will tend to cut through s/r areas, rather than provide
s/r. So, contrary to your conclusion, such charts suggest to me the need
for circular arcs. Unfortunately, there appears to be no way around the
scaling issue, but if one, as you suggest, studies the intention of the arcs and
the way they were developed then it is not clear that there is anyway around
using circular arcs when appropriate. Be that as it may, as I said before
elliptical arcs might be equal or superior to circular arcs. However,if
there is a case to be made for elliptical arcs then it will have to be doneover
time with a variety of markets and time frames, which to the best of my
knowledge has not been done. This is not a theoretical exercise, but one
of establishing whether or not a correlation exists, which will take
considerable effort to prove or disprove. At this point in time, we have a
long history associated with circular arcs and one should reject that history
with caution.</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>Bill</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV>----- Original Message ----- </DIV>
<BLOCKQUOTE
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=AR.Holzwarth@xxxx
href="mailto:AR.Holzwarth@xxxx";>AR.Holzwarth@xxxx</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=amibroker@xxxxxxxxxx
href="mailto:amibroker@xxxxxxxxxxxxxxx";>amibroker@xxxxxxxxxxxxxxx</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Tuesday, August 14, 2001 8:36
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [amibroker] Cycles</DIV>
<DIV><BR></DIV>
<DIV>"...Note that the points where the Arcs cross the price data will vary
depending on the scaling of the chart, because the Arcs are drawn so theyare
circular relative to the chart paper or computer screen. ..."</DIV>
<DIV> </DIV>
<DIV><FONT size=2>Wavemechanic,</FONT></DIV>
<DIV>your above mentioned citation from "Windows on Wallstreet" could notsay
it better. There you have the problem explained exactly as it stands. This
should convince you that in fact you want scaling-independent crossing points.
You get proper scaling-independent crossing points when you use the definition
that Dimitris has given for the arc. This is valid despite the (inevitable by
the way) fact that upon rescaling of one axis you get "illegal" circles, as
you like to call ellipses. The term "illegal circle" for an ellipseis
not very common in mathematics though. </DIV>
<DIV>Rather than doing things just "mechanically", it is important to
understand what was the original intention of the Fibonacci "circles", or
"ellipses" as they should have better called them.</DIV>
<DIV> </DIV>
<DIV>Regards</DIV>
<DIV>Alf </DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
wavemechanic
</DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=amibroker@xxxxxxxxxxxx
href="mailto:amibroker@xxxxxxxxxxxxxxx";>amibroker@xxxxxxxxxxxxxxx</A></DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Tuesday, August 14, 2001 12:36
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [amibroker] Cycles</DIV>
<DIV><BR></DIV>
<DIV><STRONG><FONT size=2>Dimitris:</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>(I assume that Cycles =
Circles)</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>Well not quite the "last lines." Your
algebra and geometry in this and previous notes are flawless, and you
clearly have conquered the equation of a circle without doing harm
to the work of the ancients. But that was never the
question.</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>What you have said about programming and
displaying a circle is exactly right. However, it is essential to
understand a tool and how it is used before programming it. As you
have discussed and shown, if you plot relative to the X & Y axis you
usually get an ellipse. This, however, is not what you want, which is
the reason that software with canned Fibonacci arcs plot relative to screen
coordinates so that a circle is displayed. Why do you suppose that
virtually all charting programs plot circular arcs at all magnifications and
time periods? This is not a matter of mathematics or
programming.</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>The problem with not plotting relativeto the
screen reflects the dual purpose that arcs are used
for. The first function is to identify support and
resistance and the second is to interact properly with line studies, in
each case providing price and time projections. Both of these
have to be effected by plotting relative to screen coordinates.
Hopefully, a picture is worth a thousand words. The attached
schematic clearly indicates that a circle on the screen is not thesame
as an ellipse with respect to either of these functions. In this
simple example, it is clear that the circular arc has provided
resistance as it should. Also, although I did not draw it in, it is
easy to imagine a line study (e.g., a tangential line) producing very
different projections for the circle and ellipse. As I said in my
Circular Fibonacci Arc note, one can use any shape on the screen that one
wants. However, based on experience circular is the way to go,
and in this business, correlations are all that we
have.</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>Remember that these techniques were used
back when everything was plotted by hand. It is up to
commercial programmers to duplicate these conditions. Unlessthis
is done one is dealing with an entirely different, untested "animal"
that may or may not be better. So far, this is not the route followed
by software suppliers. Of course, the individual can always
choose a different path and customize the arcs, especially with currently
available programs, such as AmiBroker, that are relatively easy to
program.</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG><STRONG><FONT
size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>The internet is loaded with discussions and
examples of Fibonacci Arcs with and without line studies. If you are
interested in this subject, it would be worth your time to read
about it, as well as note how other charting programs
handle the circular vs elliptical arc issue. To speed the processup
for you and others, I copied some charts from a variety of sites.
Superimpose on these images an elliptical arc and see whether it works as
well as circular with respect to support/resistance and interaction with
line studies. Perhaps this exercise will result in improved arc
formulation, use, and interpretation.</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>Hope this helped you.</FONT></STRONG></DIV>
<DIV> </DIV>
<DIV><STRONG><FONT size=2>Bill</FONT></STRONG></DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2> </FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2>Market Analyst II</DIV>
<P><SPAN style="FONT-WEIGHT: normal; TEXT-DECORATION: none"><IMG height=354
hspace=0 src="http://www.marketanalyst.com.au/help/FA.gif"; width=526
border=0></SPAN></P></FONT></STRONG>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2>Windows on Wallstreet</FONT></STRONG></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV>
<P>A common technique is to display both Fibonacci Arcs and Fibonacci Fan
Lines and to anticipate support/resistance at the points where the Fibonacci
studies cross. Note that the points where the Arcs cross the price datawill
vary depending on the scaling of the chart, because the Arcs are drawn so
they are circular relative to the chart paper or computer screen.The
following British Pound chart illustrates how the arcs can provide support
and resistance (points "A," "B," and "C").</P>
<CENTER><IMG height=263
src="http://www.geocities.com/WallStreet/Floor/1035/fibonaccistudies-1.gif";
width=380 border=1></CENTER>
<CENTER><STRONG><FONT size=2></FONT></STRONG> </CENTER>
<CENTER><STRONG><FONT size=2></FONT></STRONG> </CENTER>
<CENTER>
<P align=left><FONT face=Palantino,Times,Helvetica,Arial
size=3>Trendsoft</FONT></P>
<P align=left><FONT face=Palantino,Times,Helvetica,Arial size=3>Arcs combine
time and price to display expected containment of price action over time.
Circles are used to identify the significant high and low used for these
indicators. Note how prices found support, after the significant high at the
outer arc.</FONT></P>
<P><FONT face=Palantino,Times,Helvetica,Arial size=3>
<CENTER>
<P><IMG height=319 src="http://www.trendsoft.com/tasc/images/fib2.gif";
width=465> <BR><BR>Many analysts use arcs and fan lines together expecting
significant <BR>support or resistance to occur where these lines
cross.</P></CENTER></FONT></CENTER>
<CENTER><STRONG><FONT size=2></FONT></STRONG> </CENTER>
<DIV align=left><STRONG><FONT size=2>Stockhouse</FONT></STRONG></DIV>
<DIV align=left><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV align=left><BR></DIV>
<P align=left>
<DIV align=center><IMG height=309 alt=""
src="http://www.stockhouse.com/shfn/aug00/images/slumberger_windowonwallstreet_chart1.gif";
width=527 border=0></DIV>
<DIV align=center><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV align=left><STRONG><FONT size=2></FONT></STRONG> </DIV></DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT size=2></FONT></STRONG> </DIV>
<BLOCKQUOTE
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=TSOKAKIS@xxxx href="mailto:TSOKAKIS@xxxx";>Dimitris
Tsokakis</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A
title=amibroker@xxxxxxxxxxxxxxx
href="mailto:amibroker@xxxxxxxxxxxxxxx";>amibroker@xxxxxxxxxxxxxxx</A>
</DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Monday, August 13, 2001 3:19
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> [amibroker] Cycles</DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial size=2>Dear Bill,</FONT></DIV>
<DIV><FONT face=Arial size=2>Besides what analysts may say through you,
here is the last lines</FONT></DIV>
<DIV><FONT face=Arial size=2>on the subject.</FONT></DIV>
<DIV><FONT face=Arial size=2>Open ANY textbook to read the equation of a
circle.</FONT></DIV>
<DIV><FONT face=Arial size=2>The happy condition is that we all agree on
that the last 2500 years</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>(x-x0)^2+(y-y0)^2=R^2</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>where x0, y0 the coordinates of the center
and R the radius.</FONT></DIV>
<DIV><FONT face=Arial size=2>This, in order to be graphed, must be solved
for y and come in the</FONT></DIV>
<DIV><FONT face=Arial size=2>form y=f(x).</FONT></DIV>
<DIV><FONT face=Arial size=2>The solution is</FONT></DIV>
<DIV><FONT face=Arial size=2>y=y0+sqrt(R^2-(x-x0)^2</FONT></DIV>
<DIV><FONT face=Arial size=2>y=y0-sqrt(R^2-(x-x0)^2</FONT></DIV>
<DIV><FONT face=Arial size=2>(ask the nearest Math Department if you
doubt for the </FONT><FONT face=Arial size=2>solution)</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>For a day graph we use here</FONT></DIV>
<DIV><FONT face=Arial size=2>x=cum(1);</FONT></DIV>
<DIV><FONT face=Arial size=2>(this is the independent variable x=1, 2, 3,
etc)</FONT></DIV>
<DIV><FONT face=Arial size=2>and the code to graph a circle, centered at
(380,0) with R=20</FONT></DIV>
<DIV><FONT face=Arial size=2>is</FONT></DIV>
<DIV><FONT face=Arial size=2>/*CYCLE*/</FONT></DIV>
<DIV><FONT face=Arial
size=2>x0=380;<BR>y0=0;<BR>R=20;<BR>x=cum(1);<BR>y1=y0+sqrt(R^2-(x-x0)^2);<BR>y2=y0-sqrt(R^2-(x-x0)^2);<BR>graph0=y1;<BR>graph1=y2;<BR>graph1barcolor=graph0barcolor=2;</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>The result is graphed t w i c e
in attached gif.</FONT></DIV>
<DIV><FONT face=Arial size=2>Exactly the same cycle.</FONT></DIV>
<DIV><FONT face=Arial size=2>What you see is a cycle, has the math
properties of a cycle</FONT></DIV>
<DIV><FONT face=Arial size=2>and obeys the common for the whole world
equation of a </FONT></DIV>
<DIV><FONT face=Arial size=2>cycle.</FONT></DIV>
<DIV><FONT face=Arial size=2>With this you may solve a lot of problems,
especially if you</FONT></DIV>
<DIV><FONT face=Arial size=2>are interested for the points this circle
cuts other lines, </FONT></DIV>
<DIV><FONT face=Arial size=2>because it is the equation of the
cycle</FONT> </DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>This note in addition to #3825 Re:Angles is
covering the</FONT></DIV>
<DIV><FONT face=Arial size=2>subject sufficiently enough.</FONT></DIV>
<DIV><FONT face=Arial size=2>
<DIV><FONT face=Arial size=2>If you mind for the visual part, I have
nothing more to add.</FONT></DIV></FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Friendly yours</FONT></DIV>
<DIV><FONT face=Arial size=2>Dimitris Tsokakis</FONT></DIV><BR><TT>Your
use of Yahoo! Groups is subject to the <A
href="http://docs.yahoo.com/info/terms/";>Yahoo! Terms of Service</A>.</TT>
<BR></BLOCKQUOTE></BLOCKQUOTE><BR><TT>Your use of Yahoo! Groups is subject to
the <A href="http://docs.yahoo.com/info/terms/";>Yahoo! Terms of
Service</A>.</TT> <BR></BLOCKQUOTE></BODY></HTML>
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