
Daily Speculations 
James Sogi
Philosopher, Juris Doctor, surfer, trader, investor, musician, black belt, sailor, semicentenarian. He lives on the mountain in Kona, Hawaii, with his family. 
11/17/2005
Universal Geometry, by
Jim Sogi
It should be possible to rigorously test technical indicators to see if they are in fact informative and predictive. The million dollar question presented over the last three weeks is the extent of the current rally. This additional information is helpful as some of the quantitative statistical readings don't always give the exact entry price or exit. This is an exercise to utilize Wildberger's Universal Geometry and its appropriate use of Cartesian coordinates.
Take for illustration the simple basic upper channel TA line. Take a basic line from two retrospective chart tops (20 day highs might be an alternative). Start point A1 8/3/05 (Julian 1), 1254.50, the high swing close. The Cartesian xy coordinate is (1,1254.50).
Next point A2 9/9/05 (Julian 26) 1248.50, the next high swing close, and draw downward sloping line A1A2. Cartesian coordinate is (26,1248.50).
After A1A2, during the next month, the question became how high would the price go on this swing? When is the best time to sell the position: 1200, 1225, 1238, 1240 or 1254? In the line from the prior tops?
Does the line intersect point A3 on 11/11/05, close of 1138, the next swing high? Julian day 70 is 11/11/05. Coordinate is (70,1138). Using Universal Geometry compute whether A1A2A3 are collinear.
Take the Universal Geometry reflection calculation a la Wildberger from the xy coordinates using Julian date and price. The hypothesis is that price follows a linear regression path and upon reversal follows its reflection upon the same angle of incidence. This is another way of saying the that the rate of price rise equals the rate of decline. This allows computation by simple algebra of the coordinates that will intersect line A1A2, and the exact times and prices needed to satisfy the conditions for testing.
Add the hypothesis that the angle of reflection will equal the angle of incidence then we also have a time and date to predict the next top, and the path to get there. This should be testable, unlike old chart lines, by defining the retrospective tops, and testing whether price went to the line, but did not exceed the line, and then dropped thereafter. If significant, then test it out of sample. The use of coordinates and Universal Geometry allows rigorous definitions not previously possible.
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Jim Sogi, May 2005