1. Setting a taskAs it is known price charts on the forex market show relative price of a currency against another currency. This is the main distinctive feature of the Forex market from other markets. That’s why the value of a currency pair at any moment can be represented as a product or quotient of at least two related pairs.
For example the pair EUR/JPY can be expressed in terms of the product of the two pairs: EUR/USD and USD/JPY:
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An example of interconnection between values of currency pairs.
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Of course the market of EUR/JPY is an independent market but formation of price in the FOREX market is so structured that this formula is true practically at any moment of time.
Using this approach and having taken as basic data four main dollar pairs EUR/USD, GBP/USD, USD/JPY and USD/CHF, which I consider on the regular basis in Wave Analysis, we can set up the following system of equations:
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System of nonlinear equations
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As a result we have got a system of six nonlinear equations and ten unknowns which in addition change in course of time. From a course in mathematics it is known that such a system at each moment of time has an endless number of solutions. That’s why a mechanical search of all possible variants is a senseless task. However if we set additional conditions or limitations for this system of equation the range of possible solutions will be reduced considerably.
Projections of wave patterns which are supposed to form at the rightmost edge of the chart can act as such limitations. In this case the problem takes on a definite sense as Elliott Wave Principle may hint not only the phase of the market in which we are at this or that moment of time, not only the shape of the supposed price movement but also targets based on known proportions of the main waves inside wave patterns.
Thus the main problem reduces to solving the following sub-problems:
- 1) Determination of the additional boundary conditions of the currency pairs under consideration in the form of projections of the supposed price movement.
- 2) Determination of the key moments of time when the supposed wave patterns complete (the market’s phase).
- 3) Search of possible solution for the given system of equations at each key moments of time and within the framework of the accepted limitations.
2. Determination of boundary conditions and key moments of time The analysis of the wave picture of the currency pairs under consideration on the bigger time-frames allowed to single out three main scenarios of the possible price movement.
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Figure 1. Local correction and the subsequent completion of the previous trend.
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In the first case the previous long-term trend is broken by a forming local correction. After its completion the nearest completion of the trend itself isn’t ruled out. Such pairs as EUR/USD and EUR/GBP (upward trend), and also USD/CHF and GBP/CHF (downward trend) can be referred to this scenario.
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Figure 2. Large correction and the subsequent continuation of the previous trend.
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In the second case a long-term trend is broken by a large horizontal correction the duration of which may be considerably longer than in the first case. After the correction completes the continuation of the previous trend should be expected. Such currency pairs as EUR/JPY and CHF/JPY can be referred to this scenario.
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Figure 3. Perhaps a new trend is marked. Local correction within its framework.
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And the third scenario doesn’t rule out that a new trend has started and is developing within the framework of which a local correction is forming. Such currency pairs as GBP/USD, EUR/CHF, GBP/JPY and perhaps USD/JPY (this pair will be considered separately) can be referred to this scenario.
These scenarios and the key pulse points have determined the key moments of time where the completion of this or that wave pattern is expected. The optimal moments of time proved to be: the middle of March 2008, the second half of April 2008, the middle of summer and the beginning of autumn 2008, and the middle of the 2009 year.
At these five points of time search of appropriate solutions for our system of six nonlinear equations was implemented. And this very process took most of time spent for preparation of this article.
The calculation results are given in the following section. In spite of the fact that there are one-to-one relations between all the actual values one shouldn’t forget that this scenario is only one of possible scenarios though rather probable from my point of view.
3. The result of the solution of the system of equations at the key moments of time The results of calculations are rounded off while their actual values are shown below each chart.
3.1. Local correction and the subsequent completion of the previous trend.
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Figure 4. One of the possible variants of EUR/USD price movement
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1.48, 1.43, 1.52, 1.52, 1.38.
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Figure 5. One of the possible variants of EUR/GBP price movement.
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0.75, 0.74, 0.77, 0.76, 0.74.
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Figure 6. One of the possible variants of USD/CHF price movement.
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1.1, 1.14, 1.05, 1.05, 1.2.
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Figure 7. One of the possible variants of GBP/CHF price movement.
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2.17, 2.19, 2.07, 2.09, 2.24.
3.2. Large correction and the subsequent continuation of the previous trend.
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Figure 8. One of the possible variants of EUR/JPY price movement.
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162.8, 161.6, 156.6, 156.6, 173.9.
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Figure 9. One of the possible variants of CHF/JPY price movement.
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100, 99.1, 98.1, 98.1, 105.
3.3. New trend. Local correction within its framework.
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Figure 10. One of the possible variants of GBP/USD price movement.
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1.97, 1.92, 1.97, 1.99, 1.87.
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Figure 11. One of the possible variants of EUR/CHF price movement.
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1.63, 1.63, 1.6, 1.6, 1.66.
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Figure 12. One of the possible variants of GBP/JPY price movement.
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216.7, 217, 202.9, 205, 235.6.
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Figure 13. One of the possible variants of USD/JPY price movement.
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110, 113, 103, 103, 126.
4. Conclusion.The calculation results in the European currency pairs coincided in whole with the forecast for the 2008 year, considered in detail at the beginning of the year (refer to The review of the bigger Time-Frames and Figures 14..16, below).
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Figure 14. EUR/USD forecast for 2008. Variant 1.
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Figure 15. GBP/USD forecast for 2008. Variant 1.
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Figure 16. USD/CHF forecast for 2008. Variant 1.
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Figure 17. USD/JPY forecast for 2008. Variant 1.
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But if we compare the calculated chart of USD/JPY (Figure 13, above) with the weekly chart in Annual-08 or with the chart in the article Possible trade with an excellent profit/risk correlation, the latest calculations insistently point to possible further forming of the supposed downward diagonal triangle C of (B) of [E].
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Figure 18. Possible variant of the continuation of diagonal triangle C of (B) of [E].
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A possible variant of counting for this case is given in Figure 18. If the supposition proves to be true long positions opened in accordance with the recommendations in the article Possible trade with an excellent profit/risk correlation, should be closed as soon as the first target 113 is reached (refer to Figure 2, in the above-mentioned article ).
The wave counting of the JPY cross –rates on the basis of the last calculations may look like that.
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Figure 19. EUR/JPY forecast for 2008.
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After the historical day in 2000 the EUR/JPY pair may be forming an upward double zigzag divided by a large skewed triangle [X]. If this is the case the calculated values (refer to Figure 8, above) coincide with possible projected values defined via the size of the first zigzag [W] and the first leg (A) of [Y] of the second zigzag [Y].
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Figure 20. GBP/JPY forecast for 2008 and further.
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The GBP/JPY pair after the historical day in 1995 has formed supposedly a pair of upward impulse which can be considered as a completed zigzag or as a forming upward wedge.
In the first case one should expect a downward movement below the 140 mark. In the second case one should expect further downward correction to the area of the 180 mark with the subsequent trend reversal and forming of the ending upward impulse which will complete above the 260 mark.
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Figure 21. CHF/JPY forecast for 2008.
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After the historical day in 2000 the CHF/JPY pair may have formed an upward zigzag which is close to its completion. If this is the case the calculated values (refer to Figure 9, above) coincide with possible projected values defined via the size of the first leg [A] of the zigzag and the first wave (1) of [C] of the second leg [C] of the zigzag. Besides in this case it is reasonably to use the height of the supposed horizontal triangle (4) of [C] for specifying the projection of the ending of wave (5) of [C], that also confirms the calculated values.
Thus This article is an attempt to solve quite a complicated problem that is to say to find an acceptable solution for a system of six nonlinear equations which have in an endless number of general solutions at each moment of time. To set additional limitations with the purpose of reducing the range of search wave analysis was used as well as the method of key pulse points.
Time will show to what extent this attempt will prove to be successful.
Reference
February 23, 2008 When using any part of the article for publication or analytical materials reference to the author and Alpari is obligatory
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