## Affine geometry markets

A few years ago, I fell into the hands of some of the workshop materials on technical analysis. It was a kind <Manuscript Found in Saragossa>: without beginning or end, without the author's name. One idea contained in it, I really liked: the picture of parallel lines is mesmerizing. Then I have a lot of time tracking it on the market charts, and recently tried to program a simple transformation on the computer. The result was even more beautiful picture. It is possible that other traders will also find it food for thought and a useful guide to trade.

Price channels and memory market

In a few words, the proposed idea is to advice: If you see the chart on the market a good channel, do not forget about it, because the market and recall those channels for a long time. Sometimes, in the very distant future, it may go back exactly to the lines drawn by the channel today. Thus, the figure shows the two channels, ascending and descending, the hourly chart of Japanese yen in early 2001.

Green line shows the uplink. Vertical line labeled Up, measure its height. Accordingly, the red line is drawn down the canal and Dn - its height. With vertical lines can extend the line channels in the future, bringing them in parallel. This creates a grid of two kinds of lines. Thanks to her, it is found that, in the future if the price chart again met these lines, they will again play the role of line consolidation. In other words, to meet such a line (even after a long time), the schedule or go along it, or falling from it, and maybe even break through the line and go to the next. In any case, such a meeting signals the possibility (and direction) of the strong price move, therefore, is a signal to the open position and provides useful guidance for a profit. Not too small to trade ideas.

Indeed, in this example, the year-end chart the yen went into a long rising channel, which was no more than a projection of the ascending channel formed in the early years. The figure also marked by a dashed line middle of the channel, which often acts as a line consolidation.

Observe the different markets, it is easy to see that such behavior is not something exotic. Rather, it is a typical manifestation of the memory market and almost every significant channel can be used in this way.

Affine transformations prices

The figure is the price for a long time between the parallel lines obtained transfer lines upstream from the picture (inclined thin lines are obtained transfer lines downstream). This behavior suggests the graphics do not measure the length of the process units of time, and the length of the path traveled along the channel (in this example, the green line). Then the deviation of the graph from this direction, as measured along the lines of another channel (upward in this example), it can replace the value of the price. Figure illustrates the geometric meaning of this change of variables on the chart. It shows a new coordinate system, in which the x-axis carried out from the initial point (to, Po) in parallel to the support of the upward channel. Each point (t, P) source chart (price value P, taken at time t) can now be represented by two numbers: the distance Ox and Oy, which are derived from the design point (t, P) in the directions parallel to axes OX, OY.