OVERVIEW
Prior to our endeavors to improve the forecast for the height of third wave in a three-
wave cycle, we wish to examine some characteristics about the first two waves. In this
chapter we use 3 to 15 boxes as the reversal amounts in the swing algorithm. Again we
rely on our EURUSD database with 7,000,000+ raw tick currency prices.
A very fundamental question is: what percentage of the time do the heights of the
first and second wave equal each other in swing data? (See Table 25.1.)
First, we observe the unexpectedly high percentage of matches that occurred sig-
nifying that the heights of the first two waves are equal. This is explainable by the fact that we are dealing with discrete price differentials that have been converted to integer
pip values and is in part due to the intrinsic filtering mechanism of the swing reversal
algorithm.
Also, we note an inverse relationship between reversal amounts in the swing algo-
rithm and the percentage of matches. But this, too, appears logical after a brief period of
reflection.
Next is another logical conclusion: The percentage of matches when the height of
the first wave is greater than the height of the second wave is equal to the percentage of
matches when the height of the first wave is less than the height of the second wave.
For instance, in the table, the percentage of matches for a reversal amount of six
boxes is 25.40 percent. The percentage in this case where the height of the first wave
is greater than the height of the second wave is (100% – 25.40%)/2 or 37.30 percent.
The percentage for the case where the height of the first wave is less than the height
of the second wave is also 37.30 percent. This is because we are comparing adjacent
waves iteratively.
METHODOLOGY
In the previous two chapters, we estimated the height of the third wave by using a sim-
ple linear regression model of the form shown in Figure 25.1, where:
x=independent variable (wave 2/wave 1)
y=dependent variable (wave 3/wave 1)
A=slope
B=intercept
The linear regression model was employed because of its simplicity in calculations
and because its concept is easy to grasp. Its functionality is based on the retracement
relationship of all three waves. This has the drawback of hiding the actual magnitudes
of each wave since the dependent and independent variables are actually ratios.
In this section, we intend to enhance the forecast for the height of third wave by us-
ing the actual integer pip magnitudes instead of retracement ratios. To accomplish this,
we must regrettably incorporate an extra order of complexity into the forecasting
model.
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153
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FIGURE 25.1Linear Regression Model
MULTIPLE REGRESSION
A multiple regression is an extension of the linear regression in which the number of in-
dependent variables has been increased. See Figure 25.2, where:
x=first independent variable (height of first wave)
y=second independent variable (height of second wave)
z=dependent variable (height of third wave)
A=first partial coefficient of regression
B=second partial coefficient of regression
C=intercept or error factor
Note that there are now three regression coefficients (A, B, and C) instead of two (A
and B) as in the linear regression. This, in itself, adds a tweaking factor to the validity of
the forecast.
In plain English, this formula states that the height of one wave is dependent upon
the heights of the two preceding waves. An inexpensive beginning text on the impor-
tance of regression operations and how they work is Statistics by Murray R. Spiegel inthe Schaum’s Outline series (McGraw-Hill, 1998).
QUARTILES
In our efforts to estimate the height of the third wave that follow, we limit ourselves to the single condition that the height of the second wave must be less than the height of the first wave.
Height of wave 2 < Height of wave 1
We will, however, divide the analysis into four equal parts called quartiles. Each
quartile division will examine the retracement percentage between 0 percent and 25
percent, between 25 percent and 50 percent, between 50 percent and 75 percent, or be-
tween 75 percent and 100 percent.
In Tables 25.2 through 25.5, the column headers are defined as:
Rev Amtis the number of boxes in the swing reversal algorithm.
Swings is the number of waves in the swing data created by the reversal amount in
column 1.
FOREX SWING CHARTING
Matchesdefines the number of occurrences that satisfied the quartile conditions.
Coef A is the first partial coefficient of correlation (factor for wave 1).
Coef Bis the second partial coefficient of correlation (factor for wave 2).
Coef C is the intercept or error factor.
Std Devis the standard deviation of the dependent variable (the third wave).
Coef Cor is the coefficient of correlation between the dependent variable and the
estimate.
Before presenting some practical examples, let’s first examine the four quartile ta-
bles. The greatest number of matches with the swing data occurs when the retracement
of the first wave by the second wave (that is, wave 2/wave 1) is between 50 percent and
75 percent.
When using a three-box reversal amount, this equates to what is summarized in
Table 25.6.
We can credit the low showing of the less than 25 percent quartile to the intrinsic
nature of the swing reversal algorithm.
Also interesting to note is the fact that a retracement of less than 50 percent oc-
curred only 7.91 percent of the time while a retracement of 50 percent to 100 percent oc-
curred 93.04 percent of the time. Another interesting characteristic to the four quartile
tables is the relationship between the reversal amount and the standard deviation. As
the reversal amount increases, the standard deviation increases proportionally.
Lastly, we should note that the coefficient of correlation ranges from 84.08 percent
to 96.41 percent with an average value of 94 percent. A high coefficient of correlation
confirms that the selected forecasting model (in this case, a multiple regression with
two independent variables) is a valid representation of the real-world data.
PRACTICAL EXAMPLES
The multiple regression model is symmetrical about the x-axis. That is, it works regard-
less of whether the first wave is a bull wave or a bear wave. In the examples that follow,
the height of bull waves must be entered as positive integers and the height of bear
waves as negative integers.
Example No. 1
Reversal amount
= 3
Height of first wave
= 10
Height of second wave= –4
First we must determine which table to use by calculating the retracement percentage:
4/10 = 40 percent or the second quartile table spanning 25 percent to 50 percent. Next
locate the row containing that reversal amount:
The estimate for the height of the third wave is calculated as:
z = Ax + By + C
wave 3 = A(wave 1) + B (wave 2) + C
= (0.0773)(10) + (–0.9883)(–4) + (0.0076)
= 0.7730 + 3.9532 + 0.0076
= 4.7338
Thus the estimate for the height of the third wave is 4.7338 pips. To compute a confi-
dence level of 68 percent likelihood, we must calculate the upper and lower confi-
dence levels by adding and subtracting one standard deviation from the estimate
respectively:
Upper confidence level = 4.7338 + 1.2723 = 6.0061 pips
Lower confidence level = 4.7338 – 1.2723 = 3.4615 pips
Example No. 2
Reversal amount
= 6
Height of first wave
= –8
Height of second wave= 7
Example No. 3
Reversal amount
= 5
Height of first wave
= 12
Height of second wave= –7
Retrieve the corresponding reversal amount row from the appropriate table (7/12 =
58.33% = third quartile):
z = Ax + By + C
wave 3 = A(wave 1) + B(wave 2) + C
= (0.0140)(12) + (–1.1137)(–7) + (0.0047)
= 0.1680 + 7.7959 + 0.0047
= 7.9686
Upper confidence level = 7.9686 + 1.6877 = 9.6563 pips
Lower confidence level = 7.9686 – 1.6877 = 6.2809 pips
FIFTY PERCENT PRINCIPLE
We will also reexamine the 50 percent principle using the multiple regression model.
We performed the same analysis as used previously on the quartiles with the following
condition:
47.5% of Wave 1 < Wave 2 < 52.5% of Wave 1
and obtained the results shown in Table 25.7.
Amazingly, a 50 percent retracement occurred only about 2 percent of the time in
our 2002 EURUSD database for reversal amounts ranging from 3 to 15 boxes (a total of
61,637 matches occurred). This may appear inordinately low at first glance, but in a
volatile, news-driven market the unexpected is to be expected.
FIFTY PERCENT EXAMPLES
In Table 25.8, we set the first wave to +14 pips and the second wave to –7 pips. Column
headers are:
Estimate—the regression forecast for the height of the third wave.
Upper—the upper confidence level (estimate + one standard deviation).
Lower—the lower confidence level (estimate – one standard deviation).
Reversal amounts greater than 7 are not included in this table since the swing reversal
algorithm would automatically filter out the second wave (–7 pips).
In the table, we observe that as the reversal amount grows, the standard deviation
and the regressed estimate also grow. From this data, given a 50 percent retracement
(wave 2/wave 1), we can conclude that on average the third wave will have a height of
58.80 percent of the height of the first wave; ergo:
Average retracement for third wave = 58.80%
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