## Monday, January 24, 2011

### Monday

20:45 ET
Well I should not have tried to out guess the indicator.  The cycles came very close to being in phase, but the phase coherence failed to sync and the market continued the upward trend. This can be seen as two lines moving parallel rather than crossing in the middle sub-chart.

Someone recently told me my charts look like Tron. I saw the first one, but have yet to see the latest film.   I had to laugh because I knew what they meant. I'm like a mad scientist, and I suppose these charts are looking pretty bizarre.

Basically these studies will show Red on the Lead Wave for Bearish and Green for Bullish.  There is a lot of information concerning phase angles, but that's more for me, as I'm still trying to tweak this indicator and learn more about the phase angles.

For those of you who are interested, I have included below, a couple of web sites where you can go to see where I got my information. The math is quite complicated, but there is a description. Here are two sites I used for information.

http://cycles.technicalanalysis.org.uk/Tutorial.pdf

http://www.aspenres.com/documents/help/userguide/help/mesahelp/mesa1Using_MESA_by_John_Ehlers.html

I'll include the basic premise below.  The arrow mentioned in the first sentence is in reference to a visual aid where an arrow much like the hand of a clock is pictured.

If we let the arrow be the hypotenuse of a right triangle we can convert the description of the arrow from length and angle to two orthogonal components - the other two legs of the right triangle. The vertical component is L*Sin(θ) and the horizontal component is L*Cos(θ).
We measure the phase of the dominant cycle by establishing the average lengths of the two orthogonal components. This is done by correlating the data over one full cycle period against the sine and cosine functions. Once the two orthogonal components are measured, the phase angle is established by taking the tangent of their ratio. A simple test is to assume the price function is a perfect sinewave, or Sin(θ). The vertical component would be Sin2(θ) = .5*(1-Cos(2θ)) taken over the full cycle. The Cos(2θ) term averages to zero, with the result that the correlation has an amplitude of Pi. The horizontal component is Sin(θ)*Cos(θ) = .5*Sin(2θ). This term averages to zero over the full cycle, with the result that there is no horizontal component. The ratio of the two components goes to infinity because we are dividing by zero, and the arctangent is therefore 90 degrees. This means the arrow is pointing straight up, right at the peak of the sinewave.
One additional step in our calculations is required to clear the ambiguity of the tangent function. In the first quadrant both the sine and cosine have positive polarity. In the second quadrant the sine is positive and the cosine is negative. In the third quadrant both are negative. Finally, in the fourth quadrant the sine is negative and the cosine is positive. The phase angle is obtained regardless of the amplitude of the cycle.
An interesting observation is that if the price is a linear slope, summing the product of the price and a sine over a cycle is the discrete equivalent of the integral ∫x Sin(x) dx. Correspondingly, the real part is the equivalent of the integral ∫x Cos(x) dx. Working through these theoretical examples, we find that the phase is 180 degrees for a trending upslope and is zero degrees for a trending downslope.

15:34 ET

The Lead wave is approaching 180 degrees. I anticipate a short term sell signal will develop very soon.
12:00 ET

If you have been keeping an eye on the fork presented on Friday you know we have broken out.
Price is now at Pivot resistance and slightly above my predicted range.

The Phase Relations do not indicate an immediate change and most of my indicators are Bullish, with only a small indication on the 4Hr Phase Coherence of any weakening  (cyan bar).