Cycles review, Part IX: Cycles aspects of Gann angles and the "Square of 9" for price and time

The methods named after their founder, W. D. Gann, use angles and "fans" to project not only price but also time, and therefore can be said to incorporate or involve cycles. It also includes calculations involving the Square of Nine, so I'm associating it to this Part IX in my review of cycles methods! Gann wrote a publication about his angles method, The Basis of My Forecasting Method, in 1935. I'm glad to see that Andy Askey has made a couple of recent posts at his PTV-Investing Blog, which we can reference to illustrate some information on Gann analysis. One is Linear Square of Nine on SP500 Index (4/1/09). Another is Low Volume Thrust - Need Continuation Follow Through (5/18/09) which includes Andy's comment, "The SP500 index (SPX) met the 218 day cycle with buying - but not with enthusiasm." Below is one of his charts that accompanies that post, and you can see that this particular chart takes an extra step to really illustrate how the angles can be used with cyclic elements. (It reminds me to an extent how I've built up my trendlines on the VIX chart - not specifically attempting Gann analysis but there may be similarities.) Another post by Andy there is Crude Oil Bounce Is Weak In Long Term (5/19/09). You'll want to read his complete posts to learn more about this, of course. But for a quick look at how he puts Gann analysis into action, here's a quote from the post about oil:

How high can we reasonably expect the current bounce to move? The
quick and simple answer is the 50% price retrace level near $90. The
probability of a complete retrace in the short term is very low as the bounce is
less that half as strong as the move down. But a move to a 50% retrace at
100% time cycle this summer is not out of the question. In the long term
this bounce is tepid and shows few believe the 2008 high was anything more than
a blow off of the long term trend. Still a move from 60-90 is a 50% move
in price and and a chance for traders to make money in this sector.

The "Square of 9" Andy describes briefly: "Market prices tend to move according to a square root algorithm. This occurs over and over again and can be found on the SP500 Index (SPX) without trying very hard. Gann did not have access to an electronic calculator, spreadsheets, computers, or anything we take for granted today. In his day, the square of 9 was an amazing tool for finding natural price resistance and time cycles from a specific point. It continues to work today." Andy shows an example at this post, Gann Wheel or Emblem from March 6th Low (4/30/09)(and his graphic there looks neat so I've included it, at right - read his post there for more information for using it). In Andy's post about the Square of Nine on the long-term S&P 500 chart (referenced with link in the opening paragraph above), here are Andy's comments on the big picture in the S&P 500 index:

The price action from 2002 has consistently followed the square root
progression. Price topped at six complete cycles of 360 degrees in October
2007. The March low came very close to 360 degrees below the 2002
low. Maybe price has unfinished business… maybe not. Near 880 is 720
degrees off the low and a place to watch for this leg to stall out.

Andy provides additional information about the Square of Nine in this post at his site: Gann Square of 9 (12/23/08). There's actually some information on Gann and his angles, at http://en.wikipedia.org/wiki/Gann_angles too. Below are some of Andy's charts that go along with the posts referenced above. First, his big-picture view of the S&P 500 in the Square of Nine post; next, one from his May 18 post about the possibility of the SPX doing a 50% retrace on a pullback; and at bottom is his chart associated with his post about oil: