OVERVIEW
In the preceding chapters, we analyzed some concepts on how to estimate the height of
the third wave in a three-wave cycle when the heights of the first two waves are known.
In the current chapter, we will extend this idea one logical step further and attempt to es-
timate the height of the fourth wave based on the known heights of the first three waves.
TESTING APPROACH
We will again employ an ordinary least squares (OLS) multiple regression, this time us-
ing the model with three independent variables. See Figure 26.1, where
w=the first independent variable (height of first wave)
x=the second independent variable (height of second wave)
y=the third independent variable (height of third wave)
z=the dependent variable (height of fourth wave)
A=the first partial coefficient of regression
B=the second partial coefficient of regression
C=the third partial coefficient of regression
D=intercept or error term
Note that we are now dealing with four regression coefficients (A, B, C, and D),
which definitely increases the complexity of the mathematical operations involved
(specifically, the solution to simultaneous equations).
Given a known three-wave bull cycle, we label the four heights as w, x, y, zwith the
objective of estimating the height z. (See Figure 26.2.)
In Table 26.1, we have calculated the values of the four regression coefficients
based on anypossible three-wave cycle. That is, there are no constraints on retrace-
ment percentages between any two adjacent waves. We scanned the EURUSD database
sequentially for every four-wave combination.
PRACTICAL EXAMPLES
Example 1: Three-Box Reversal Amount, Wave 1 = 10,
Wave 2 = –5, Wave 3 = 7
Wave 4 = A(Wave 1) + B(Wave 2) + C(Wave 3) + D
= (–0.3700)(10) + (–0.0786)(–5) + (–0.6785)(7) + (–0.0008)
= –3.7000 + 0.3930 – 4.7495 – 0 .0008
= –8.0573
(See Figure 26.3.)
Example 2: Five-Box Reversal Amount, Wave 1 = –8, Wave 2 = 3,
Wave 3 = –6
Wave 4 = A(Wave 1) + B(Wave 2) + C(Wave 3) + D
= (–0.3104)(-8) + (0.1445)(3) + (–0.5251) (–6) + (–0.0021)
= 2.4832 + 0.4335 + 3.1506 – 0.0021
= 6.0640
IMPROVING THE FORECAST
As stated previously, the coefficients in the preceding table can be applied to any three-
wave cycle to forecast the height of the fourth wave. The disadvantage to such a generic
approach is that, even though the forecasts are intrinsically accurate, the standard devi-
ation is very high, which widens the channel of confidence too much to be of serious
practical use. In other words, the further the upper confidence level and the lower confi-
dence level are from the estimate, the less reliable the forecast.
164
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FIGURE 26.3IDVhytF GlW k
For that purpose, we decided to analyze two basic and distinct three-wave patterns
with the premise that their common characteristics will generate similar forecasts for
the fourth wave with a smaller standard deviation. The patterns are a three-wave trend-
ing cycle and a three-wave nontrending cycle.
THREE-WAVE TRENDING CYCLES
This cycle consists of two complementary patterns, which are displayed in Figure 26.4.
In the case of the bull cycle on the left, the inequality constraints are:
A < C < B < D
The bear cycle on the right has the following constraints:
A > C > B > D
The coefficients of regression for the height of the fourth wave for bothbull and bear
trending patterns are calculated in Table 26.2.
TRENDING EXAMPLE
As noted previously, the heights of bull waves must be entered as positive integers,
while the heights of bear waves must be entered as negative integers.
Reversal Amount= 4 Boxes, Wave 1 = +9, Wave 2 = – 4, Wave 3 = +7
Wave 4= A(Wave 1) + B(Wave 2) + C(Wave 3) + D
= (–0.2014)(9) + (0.2190)(–4) + (–0.5782)(7) + (–0.0209)
= –1.8126 – 0.8760 – 4.0474 – 0 .0209
= –6.7151
THREE-WAVE NONTRENDING CYCLES
These cycles (known as contracting triangles) consist of two symmetrical patterns,
which are displayed in Figure 26.5.
In the case of the contracting triangle on the left, the inequality constraints are:
A < C < D < B
The contracting triangle on the right has the following constraints:
A > C > D > B
The coefficients of regression for the height of the fourth wave for both contracting
triangle patterns are calculated in Table 26.3.
NONTRENDING EXAMPLE
Reversal Amount = 3 Boxes, Wave 1 = –10, Wave 2 = +8, Wave 3 = –5
Wave 4 = A(Wave 1) + B(Wave 2) + C(Wave 3) + D
= (–0.3387)(–10) + (–0.1737)(8) + (–0.7909) (–5) + (0.0084)
= –0.3387 – 1.3896 + 3.9545 + 0.0084
= 2.2346
EXTENDING THE FORECAST
It is possible to forecast the height of the fifth wave from a three-wave cycle using the
information in this chapter. Simply follow the preceding procedure to estimate the
height of the fourth wave. Next make the following substitutions:
Let new wave 1 = old wave 2.
Let new wave 2 = old wave 3.
Let new wave 3 = estimate for wave 4.
Then repeat the procedure. However, the disadvantage to this method is that the stan-
dard deviation of the estimate increases with each new iteration and the reliability of
each new forecast decreases significantly.
ESTIMATE CHARTS
In Figure 26.6, the bold solid line represents swing data using a three-box reversal
amount for the EURUSD currency pair during January of 2002. The lighter dotted line
represents the estimate of the fourth wave using the regression analysis described
in this chapter. The zero-mean oscillator at the bottom of the chart represents the
error of the estimate (the swing data value minus the corresponding fourth wave
estimate).
In Figure 26.7, the reversal amount has been increased to seven boxes for
comparison.
One simple observation about these two swing charts is that as the reversal amount
increases, the error of the estimate increases proportionately. Increasing the reversal
amount also generates fewer waves for the same time frame, although this was to be ex-
pected in retrospect.
Many traders are probably curious about the effect of large reversal amounts on the
error of the estimate. For that purpose, we present one more swing chart in Figure 26.8,
this time with a 15-box reversal amount.
LIVE USAGE
Traders will note that there is a wealth of information in this chapter and will probably
wonder just how to apply these new concepts to an actual trading session inside the
currency dealer’s online trading platform.
First, a pencil and a sheet of graph paper are required. Some traders may find a six-
inch transparent ruler helpful when measuring price movements directly on the moni-
tor. Traders familiar with point and figure charting methods should have no problem.
We recommend the following initial steps:
1.Display the EURUSD currency pair in the trading platform window.
2.Set the time interval in the window to a minimum, such as 5, 10, 15, or 30 seconds.
3.Mentally set the box size to one pip.
4.Set the reversal amount to three boxes (again mentally).
5.Begin plotting the Xs and Os in the point and figure chart.
6.If a distinguishable match between the P&F pattern and either a three-wave trend-
ing pattern or a contracting triangle occurs, then refer to the corresponding table in
this chapter and perform the necessary arithmetic to calculate the height of the sub-
sequent wave. Mark the estimate on the graph paper and set up an imaginary stop-
loss limit order and an imaginary take-profit limit order.
7.Continue plotting Xs and Os until the objective is attained or a stop-loss level is en-
countered.
Note that this method might take numerous paper trades before traders are com-
fortable with this form of trading. Also, we chose a box size of one pip and a three-box
reversal amount simply as a beginning exercise. Traders should base their choices on
the magnitude of the bid/ask spread of the underlying currency pair, the current volatil-
ity of that pair, familiarity with P&F techniques, and individual trading goals.
Traders should save each completed sheet of graph paper for subsequent scrutiny.
Date, time, currency pair, box size, reversal amount, arithmetic calculations, the esti-
mate, and the actual outcome should all be logged directly on the graph sheet.
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