OVERVIEW
In this chapter we examine some very fundamental characteristics about cycles: how
frequently they recur and in what percentages. The identification criteria that distinguish one cycle from the others will be the inequality constraints between the vertices
(peaks and valleys) of each cycle. The lower-case letters, a, b, c, d, and so on, represent
discrete prices and not the heights of individual waves. The upper-case letters, A, B, C,
D, and so on, will be used to identify the different cycle patterns within a family of cy-
cles. (See Figure 27.1.)
TWO-WAVE CYCLES
When scrutinizing two-wave cycles, we see in Figure 27.2 that there are only six permutations if we use the mathematical operators <, > and =.
The identifying criteria for the two-wave bull cycles are:
Cycle A
a < c < b
Cycle B
a = c < b
Cycle C
c < a < b
The identifying criteria for the two-wave bear cycles are:
Cycle D
a > c > b
Cycle E
a = c > b
Cycle F
c > a > b
Using the 7,000,000+ EURUSD tick database, the results were calculated as shown in
Table 27.1.
The columns labeled A through F represent the percentage of occurrences for the
corresponding cycle. Thus, summing these columns in each row will equal 100 percent.
The salient feature about this table is that the two symmetrical cycles, B and E, decrease
in frequency as the reversal amount increases. The remaining cycles occur with nearly
identical frequencies, which is to be expected since they are bull-bear inverse cycles.
THREE-WAVE CYCLES
When analyzing cycles with three or more waves, it is more expedient to ignore
cycles in which two vertices are equal. We focus solely on the “greater than” and
“less than” conditions. Therefore, we examine only the three-wave cycles shown in
Figure 27.3.
The inequality constraints for the cycles are:
Cycle A
a < c < b < d
Cycle F
a > c > b > d
Cycle B
a < c < d < b
Cycle G
c > a > b > d
Cycle C
c < d < a < b
Cycle H
c > d > a > b
Pater nFrqurctirs
173
TABLE 27.1-ne(deAOser )Freb oA PeEenrFX UWodAlr
Cycle D
c < a < d < b
Cycle I
c > a > d > b
Cycle E
c < a < b < d
Cycle J
a > c > d > b
The first noteworthy feature in Table 27.2 is the very low frequencies for cycles C
and H, although they do increase geometrically as the reversal amount increases lin-
early. Cycles D and I are the table leaders, although both are components of longer
lateral movement cycles. Erroneously, we expected the ideal bull cycle (A) and the
ideal bear cycle (F) to exhibit slightly higher table frequencies, but intuition is not always correct.
FOUR-WAVE BULL CYCLES
In order to limit the number of cycles examined, we again ignore cycles where any two
vertices are equal. Also we confine our analysis to bull formations only in this section.
Bear cycles are examined in the following section.
The first seven four-wave cycles that we examine are bull cycles in which the height
of the first wave is greater than the height of the second wave. (See Figure 27.4.)
The inequality constraints are:
Cycle A
a < c < b < e < c < e < b < d
Cycle C
a < e < c < b < d
Cycle D
e < a < c < b < d
Pater nFrqurctirs
175
TABLE 27.2-ne(deAOser kon ifneetTFEe uhOXer
Cycle E
a < c < e < d < b
Cycle F
a < e < c < d < b
Cycle G
e < a < c < d < b
Examination of Table 27.3 reveals that the ideal bull cycle (cycle A) has a rather
low percentage of occurrences. Trend followers are happiest when the trend in
which they have invested continues for more than three cycles. The obvious winner
is cycle B, a bull cycle in which the last wave has dipped slightly below vertex b.
However, this is not an omen of any sort, particularly if the first three waves are
treated as a single bull wave. The distribution of the remaining cycles is somewhat
unimpressive. One key observation, though, is the effect of reversal amount on indi-
vidual columns.
FOUR-WAVE BEAR CYCLES
Again we will limit the number of cycles to examine by ignoring cycles where any two
vertices are equal. The first seven four-wave cycles that we examine are bear cycles in
which the height of the first wave is greater than the height of the second wave. (See
Figure 27.5.)
The inequality constraints are:
Cycle A
a > c > b > e > d
Cycle B
a > c > e > b > d
Cycle C
a > e > c > b > d
Cycle D
e > a > c > b > d
Cycle E
a > c > e > d > b
Cycle F
a > e > c > d > b
Cycle G
e > a > c > d > b
The observations with regard to the four-wave bull cycle table (Table 27.3) apply in
Table 27.4 too; simply keep in mind the effect of the bull-bear inverse relationship. Sta-
tistically, the two tables are very similar.
USAGE
Cycle frequencies analysis should not be employed as a trading system unto itself since it is purely a mechanical percentage technique. Nonetheless, knowledge of these percentages of likelihood may assist traders in the decision-making process when coupled with other signal-generation systems.
Also, we must note that the tables in this chapter pertain specifically to the raw tick data for the EURUSD currency pair during the 2002 calendar year. However, they do ex-
hibit a sort of generic quality that may be used as a template for other currency pairs.
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