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In the construction of affine schedules to meet another complication - negative price. To avoid the associated distortion candlestick chart is proposed to move the affine charts in the positive region (adding 20,000 in the case of 1000 and JPY_RIS JPY_FAL).

Figure illustrates this property of memory channels to another example - the hourly chart of the euro.

Use in trade

The basic properties of affine chart following the method of their construction. _RIS Support level on the chart with the line of the bullish trend on the original price chart, which is parallel to the line of the generating channel. Resistance at _FAL chart shows that the price is falling trend line parallel to the direction of the generating downlink. Breakthrough affine level gives a strong signal, and the longer the level, the greater the progress prices should be expected after his breakthrough.

Of course, all this is well-known properties of market charts, but affine projections can do a lot of price movement more visible and predictable. In addition, there are new non-trivial options trading decisions. Below are just some possible ideas for using affine charts.

Affine projection and technical figures. In technical analysis, we know many different <figures>, whose appearance on the charts predict possible future course of prices. In some cases, the body forming the affine chart may show better than the original. And often figure, clearly visible on the affine chart prices, the source can not be formed at all. This situation is illustrated by the example of figure drawing <folding rule>.

According to the interpretation of the tape measure (see [1]), we have three clear buy signal on the affine versions JPY_RIS (breakouts rays 1, 2, 3), while in the original graph yen folding rule does not appear at all, and here much more difficult it would be to get the same trading signals.

Affine projection and the Fibonacci ratio. A very interesting example of the balance of the Fibonacci chart and its affine version is shown in Figure (bottom here - JPY_FAL). JPY_FAL return to its previous high (100%) and a break of this level - strong buy-signal - has no counterpart in the original price chart, so here are the use of affine projection provides an opportunity not to miss this favorable moment to go long.

The subsequent breakthrough level of 161.8% on JPY_FAL (Fibonacci projection) coincided with a breakthrough level of 61.8% on the chart, which can be seen as further evidence of the strength of this buy-signal. Affine projection and other indicators. One example of a union of affine projection with other indicators for trading signals shown in the figure (marked rectangles are magnified graphics faster euro and its affine version EUR_FAL 2-3 January 2002).

Indicator RSI c option 8 on the affine chart EUR_FAL gave a clear sell signal in the form of a bearish divergence. Open at the signal position could bring good income (after highs reached on January 2, the euro fell below the end of the month 0.86). At the same time on the original price chart divergence is absent (the line drawn on the chart euros through two local maxima, pointing down, not up, as EUR_FAL). In conclusion, the formation of the parallel lines of the consolidation and long-term preservation of their power is a direct consequence of the properties of the memory market. Affine transformations of price charts to help make this more explicit geometric picture. Although from a mathematical point of view, it's just the equivalent representation, no more than another point of view, but to make trading decisions, it may be no less important than the schedule. Affine projection is given more than one, but two new point of view! Combining affine versions with different analytical tools, you can find a lot of useful trading ideas.

## Affine geometry markets

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