of the rule occur atall price levels or matrices, and many are being worked simultaneously in any given ongoing market (Figure 15-5).
Goodman Swing Count System
Figure 15-4 The Measured Move and Unwinding.
Figure 15-5 The Markets Are Recursive.
99
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Part 4: Brief History of Wave Theory
This is a critical point. In modern terminology, it would be saidthat price movements are recursive. Simply stated, this means thatwithout labeling, you cannot really tell the difference between a10-minute chart and a daily or weekly chart.
CARDINAL PRINCIPLESThe GSCS has six cardinal principles.1.
Price Surge
Goodman realized both the possibilities for a reversal (as in thecase of the completed measured move) and a price surge. A pricesurge would be the equivalent to the sellers (in an uptrend) andthe buyers (in a downtrend) winning the tug of war within amatrix. In price action, this means that prices would fall or rise toat least the beginning point of the initial swing.2.
Multiple-Level Matrices
Goodman discovered the implications of the rule occurringsimultaneously at all price levels. This is equivalent to the fractalproperty in other wave systems.3.
Compensation
The extent that a price swing overshoots or undershoots its ideal50 percent retracement will be “made up” on the next price swingwithin the matrix. For example, if prices fall by only 40 percent ofthe initial trend and reverse, the measured move actually will beeither 90 or 110 percent of the measured move point and valueof the primary (initial) swing in the matrix. The 10 percent difference—the GCSC holds—must be made up eventually. This is theconcept of compensation.
4.
Carryover
Furthermore, if the difference is not fully made up in the finalprice swing of a matrix, the cumulative “miss” value will carry over
Goodman Swing Count System
101
through each subsequent price matrix until it does. This is theconcept of carryover. A carryover table is used to add and subtractcumulative carryover values until they cancel.
5.
Cancellation
When no carryover remains, the price matrix is said to havecleared or canceled. This is the GCSC concept of cancellation. It iscritical to finding GCSC support and resistance points and otherchart hot spots where something much less than random is likelyto occur.
6.
Intersections
The importance of a hot spot in relationship to its likelihoodof being an important point of support or resistance or reversalor continuation increases when two or more price matrices cancelat the same price or in the same price area. This is the key concept of intersection. There is no analogous concept in Elliott wavetheory, the most common competitor to the GSCS. Intersectionmakes the GSCS much more objective and testable than otherswing systems.
CAVEATAll new systems almost always possess a few unresolved quirks andareas of uncertainty. Nonetheless, the GSCS offers tremendouspotential for dedicated traders who wish to pursue its intricaciesand do the necessary testing. This chapter is simply a summary ofsome of the salient features. Michael D. Archer offers comprehensive lectures on the GSCS at www.fxpraxis.com.
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5
PARTTwo-WaveCycles
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Chapter
16
Properties ofTwo-Wave CyclesOVERVIEWEarlier we defined a wave as single diagonal line representing theslope between two price extremes and a cycle as a series of two ormore waves. Our analysis logically begins with the smallest cyclepossible, two consecutive waves. The criterion for comparing twowave cycles is the ratio of the heights between adjacent waves. Thethree obvious conditions are therefore greater than, equal to, and lessthan (Figures 16-1 through 16-3).Each of these diagrams has two cycles. The cycles on the left arereferred to as bull cycles, and the cycles on the right are called bear
Figure 16-1 Wave 1  Wave 2.105Copyright © 2007 by The McGraw-Hill Companies. Click here for terms of use.
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Part 5: Two-Wave Cycles
Figure 16-2 Wave 1  Wave 2.
Figure 16-3 Wave 1  Wave 2.
cycles. The direction of the first wave in a cycle determines the useof bull/bear nomenclature throughout this book.
FREQUENCIESIn Table 16-1, the two-wave relationship frequencies are expressedas percentages for several minimum reversal amounts.Table 16-1 Two-Wave Relationship FrequenciesNo. Relationship123
5-Pip
10-Pip
15-Pip 20-Pip
25-Pip 30-Pip 35-Pip
Wave 1  wave 2 33.34Wave 1  wave 2 33.39Wave 1  wave 2 33.26
42.8616.2040.93
47.465.9146.63
48.471.6649.89
48.473.4748.06
48.47 47.851.16 1.1249.57 51.03
Properties of Two-Wave Cycles
107
It is assumed that relationships 1 and 3 will approximate eachother automatically when a large sample is analyzed. This table isincluded here simply to display the decreasing values for theequality relationship as the minimum reversal amount increases.For example, using a 20-pip minimum reversal amount, there isonly 3.5 percent likelihood that two adjacent waves will be equalin height.
BASIC MODELThe first test is to determine if the heights of any two consecutivewaves provide sufficient data to forecast the height of the subsequent wave accurately. This uses the generic linear autoregressivemodel, namely,Z t +1 = AZ t −1 + BZ t + εtand more specifically,Wave 3 = A × wave 1 + B × wave 2Where A  first partial coefficient of regressionB  second partial coefficient of regressionε  error factor
INITIAL TESTThe first step is to convert the 29 million  streaming quotes inour EURUSD 2005 database into swing data using variousminimum reversal amounts. By applying an ordinary least squares(OLS) regression to the swing data, the results shown inTable 16-2 were obtained.The column headers are defined as follows:Rev Amt—the minimum reversal amount used in the swingreversal algorithmNo. Waves—the number of diagonals created by the swingalgorithm
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Table 16-2 Autoregressive Partial CoefficientsRev Amt
No. Waves
Mean Ratio
A
B
SEE
COR
5101520253035404550
912,38561,96111,6324,7882,6561,6401,164850668538
1.03381.06261.12021.15191.16191.74431.17421.17741.17311.1759
0.26740.34520.33960.32280.29330.31700.33300.29580.31890.3180
0.75730.69600.73990.77970.81990.80090.78050.82900.79720.7984
0.26830.37920.54850.62760.65500.68020.66740.72200.68960.6906
26.9334.1233.7432.8530.1932.2735.4029.3532.9634.12
Mean Ratio—the average ratio of the third (extrapolated)wave divided by the second waveA—the partial regression coefficient for the first waveB—the partial regression coefficient for the second waveSEE—standard error of the estimateCOR—the coefficient of regression expressed as a percentage
INTERPRETATIONStatistically, the results in Table 16-2 are not surprising, as definedby the crucial final column, the coefficient of correlation. Anaverage value of 31 percent indicates that less than one-third theheight of the third wave can be attributed directly to the heightsof the two previous waves. The generic model above therefore isinadequate as a valid third-wave forecaster.
Chapter
17
Enhancing theForecastOVERVIEWThe basic autoregressive model discussed in Chapter 16 is toogeneric to serve a useful purpose under certain circumstances.Therefore, some simple constraints must be imposed on the relationship between the first and second waves. Our new approachis to create three separate tests using the following heightrelationships:Test A: Height of wave 2 less than one-third the height ofwave 1Test B: Height of wave 2 greater than one-third the height ofwave 1 and less than two-thirds the height of wave 1Test C: Height of wave 2 greater than two-thirds the height ofwave 1 and less than the height of wave 1
FIRST-TERCILE TESTINGIn Tables 17-1 to 17-3, the values in the “Mean Ratio” columnare calculated as the height of wave 3 divided by the height ofwave 1.
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Part 5: Two-Wave Cycles
Table 17-1 First-Tercile Regression CoefficientsRev Amt No. Waves510152025
37620815910868
Mean Ratio
A
B
SEE
COR
0.34650.41410.42130.42210.4051
0.11640.02910.04930.14700.1041
0.82921.38321.32650.99521.8477
0.12260.17630.18610.17090.2101
87.7482.3781.3982.9178.99
Table 17-2 Second-Tercile Regression CoefficientsRev Amt510152025
No. Waves
Mean Ratio
A
B
SEE
COR
46,0215,6021,904865507
0.65740.68290.72010.73650.7304
0.04220.14740.08280.01960.0194
1.08460.98431.20511.46191.4538
0.16990.26300.33520.38470.3723
83.0173.7066.4861.5362.77
Table 17-3 Third-Tercile Regression CoefficientsRev Amt
No. Waves
Mean Ratio
A
B
SEE
COR
510152025
257,83420,7473,4571,347711
0.87690.96351.04651.07231.1161
0.35230.27170.42560.54930.4020
0.64830.83150.75030.63410.8634
0.22090.32790.49350.54050.6140
77.9167.2150.6545.9538.60
USEFirst, we observe that partitioning the sample data into threeequal divisions has greatly enhanced the coefficient of correlation,particularly in the first tercile. To illustrate that these tables canbe put to practical use, we include the following example.Assume that we employed a 10-pip minimum reversal amountto create the swing data. Also assume that the last two known wavesin the swing data are 19 and 12 pips, respectively. Since 12 isgreater than one-third of 19 and less than two-thirds of 19, we use
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Enhancing the Forecast
the second-tercile table to calculate the height of the next wave.We use the basic modelWave 3 = A × wave 1 + B × wave 2and substitute our known wave heights:Wave 3 = A × 19 pips + B × 12 pipsNext, we replace A and B with the corresponding values in thesecond-tercile table:Wave 3 = 0.1474 × 19 pips + 0.9843 × 12 pipsThen we multiply the coefficients:Wave 3 = 2.8006 + 11.8116and add the two products:Wave 3 = 14.6122Thus there is a 74 percent likelihood (the coefficient of correlation) that the next wave will be 15 pips in height (Figure 17-1).
Figure 17-1 Third-Wave Forecast.
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There is a quicker (though less accurate) method to calculatethe height of the next wave. Simply multiply the height of the firstwave by the corresponding mean ratio in the table:Wave 3 = wave 1 × mean ratioWave 3 = 19 pips × 0.6829Wave 3 = 13 pipsThe analytical approach illustrated in this chapter may appearsomewhat simplistic to some traders. However, it is necessary inorder to lay down a foundation for more advanced forms of ratioanalysis and autoregression used in later chapters.
6
PARTThree-WaveCycles
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Chapter
18
Basic Types ofThree-WaveCyclesOVERVIEWAs in Chapter 17, the criterion for identifying a basic three-wavecycle is the relationship between the heights of the individual wavesusing the three comparison operators: greater than equal to less thanThese operators define nine unique bull cycles and nine uniquebear cycles. If the first wave in any cycle is upward, then the entirecycle is referred to as a bull cycle. If the first wave in any cycle is downward, then the entire cycle is called a bear cycle. Each three-wave cycleis identified by a one-letter label (ID). Bull cycles use the uppercaseletters “A” through “I,” whereas bear cycles are designated by thelowercase letters “a” through “i.”
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Part 6: Three-Wave Cycles
IMPULSE CYCLE (ID  A)The single most important three-wave cycle is called an impulsecycle, a term borrowed from the Elliott wave principle. This patterndefines a clear and consistent trend in either price direction. Thecycle begins with a price surge followed by a retracement wavewhose height is less than the height of the initial surge wave. Theheight of the final wave must exceed the height of the retracementwave (Figure 18-1).
Figure 18-1 Impulse Cycle.
RECTANGLE (ID  B)The second three-wave cycle occurs less frequently than theimpulse cycle because the heights of all three waves must be thesame. The rectangle formation represents a horizontal price movement, also called lateral congestion (Figure 18-2).
Figure 18-2 Rectangle.
Basic Types of Three-Wave Cycles
117
CONTRACTING DESCENDINGTRIANGLE (ID  C)This cycle is identified as two waves of the same height followed byone wave whose height is less than either of its two predecessor waves(Figure 18-3).
Figure 18-3 Contracting Descending Triangle.
CONTRACTING ASCENDINGTRIANGLE (ID  D)This cycle is identified as a price-surge wave followed by two waveswhose heights are equal to or less than the height of the initial wave(Figure 18-4).
Figure 18-4 Contracting Ascending Triangle.
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Part 6: Three-Wave Cycles
CONTRACTING SYMMETRICALTRIANGLE (ID  E)This cycle is identified as an initial price-surge wave followed bytwo waves whose heights are less than the immediate predecessorwave (Figure 18-5).
Figure 18-5 Contracting Symmetrical Triangle.
EXPANDING ASCENDINGTRIANGLE (ID  F)This cycle is identified as two waves whose heights are equalfollowed by a final wave whose height is greater than either of itspredecessor waves (Figure 18-6).
Figure 18-6 Expanding Ascending Triangle.
Basic Types of Three-Wave Cycles
119
EXPANDING DESCENDINGTRIANGLE (ID  G)This cycle is identified as an initial wave whose successor wavesare both greater than the initial wave but equal to each other(Figure 18-7).
Figure 18-7 Expanding Descending Triangle.
EXPANDING SYMMETRICALTRIANGLE (ID  H)This cycle is identified as an initial price-surge wave followed bytwo waves whose heights are greater than the immediatepredecessor wave (Figure 18-8).
Figure 18-8 Expanding Symmetrical Triangle.
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Part 6: Three-Wave Cycles
CONNECTOR (ID  I)This cycle is so named because it links two impulse cycles togetherto create an even longer trend cycle. The height of the middlewave is always greater than the heights of either two adjacent waves(Figure 18-9).
Figure 18-9 Connector.
BEAR-CYCLE CONVERSIONEach three-wave bull cycle can be converted to an equivalent bearcycle simply by rotating the cycle 180 degrees along its x axis (or innontechnical parlance, “flipping” the cycle vertically). The heightcomparison constraints remain the same, but the first wave nowpoints downward. Four of the triangle designations become reversed,as shown in Table 18-1 (reversed names are displayed in italics).
FREQUENCIESTable 18-2 expresses the frequencies of the three-wave cycles as percentages for several minimum reversal amounts. Bull and bearcycles have been added together.Several interesting cycle properties are exhibited in this table.As the minimum reversal amount for the swing algorithmincreases, two seemingly opposite phenomena occur:1. The frequencies of the impulse cycles, both symmetrical triangles, and the connector cycles also increase.2. The frequencies of the rectangles, both ascending triangles, andboth descending triangles decrease.
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Basic Types of Three-Wave Cycles
Table 18-1 Bear-Cycle ConversionsNo.
Bull Name
ID
Bear Name
ID
123
ImpulseRectangleContracting DescendingTriangleContracting AscendingTriangleContracting SymmetricalTriangleExpanding AscendingTriangle
AB
ImpulseRectangle
ab
C
Contracting AscendingTriangleContracting DescendingTriangleContracting SymmetricalTriangleExpanding DescendingTriangle
c
Expanding AscendingTriangleExpanding SymmetricalTriangleConnector
g
456789
DEF
Expanding DescendingTriangleExpanding SymmetricalTriangle
H
Connector
I
G
def
hi
The reason for this is quite simple: The cycles that decrease infrequency all have equality relationships between the heights oftwo or more waves in those cycles. Naturally, as the heights of twoadjacent waves increase, there is less likelihood that they will bethe same magnitude because the y-axis resolution is growing moreand more graduated. Mathematically, this is analogous to the outcome of throwing different numbers of dice. Tossing two dice at
Table 18-2 Three-Wave-Cycle FrequenciesID
Cycle Name
ABCDEFGHI
ImpulseRectangleCon Desc TriangleCon Asc TriangleCon Sym TriangleExp Asc TriangleExp Desc TriangleExp Sym TriangleConnector
5-Pip 10-Pip 15-Pip 20-Pip 25-Pip 30-Pip 35-Pip13.312.87.613.16.913.07.56.918.9
22.93.74.28.611.38.33.99.727.3
29.50.61.73.514.53.61.813.631.6
30.90.20.82.215.42.41.114.732.2
31.80.00.51.515.71.20.616.932.3
32.50.10.40.716.10.70.416.232.9
33.70.00.30.713.50.80.416.634.0
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Part 6: Three-Wave Cycles
one time renders 36 possibilities. Throwing four dice at the sametime generates 1,296 possibilities (thus greater gradation).One more curiosity can be observed in Table 18-2. In all thedifferent minimum reversal amounts, the connector cycle alwaysranked at the top of the list in frequency count, even surpassing theimpulse cycle that we originally expected to head the list. This factwill be useful in later studies.
Chapter
19
Forecasting theThird WaveFORECASTING WAVE RELATIONSHIPSTable 18-1 in the preceding chapter not only exhibits thefrequency data for three-wave cycles but also provides sufficientinformation to forecast the logical length of the third wave whenonly the first two waves are known. By logical length, we mean theresult of the comparative ratio length using the logical operators, , and  .
PRACTICAL EXAMPLEFor example, assume that the final two waves in the swing dataform the pattern shown in Figure 19-1.We automatically know that there are three possible continuations once the next wave is known: an impulse cycle, a contracting ascending triangle and a contracting symmetrical triangle(Figure 19-2).From Table 18-1, we obtain the percentages for a 35-pip reversalamount for the possible continuations, as shown in Table 19-1.
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Part 6: Three-Wave Cycles
Figure 19-1 Two-Wave Pattern (Wave 1  Wave 2).
The next step is to sum the percentages in Table 19-1 and dividethat sum into each value (Table 19-2):33.7 + 0.7 + 13.5 = 48.9Given the two-wave pattern in Figure 19-1, this means that whenusing a 35-pip swing reversal amount, there is a 69 percent likelihood that the next wave in the swing data will surpass the top ofwave 1 and become a “full” three-wave impulse cycle.
Figure 19-2 Possible Third-Wave Continuations.
125
Forecasting the Third Wave
Table 19-1 Raw PercentagesCycle NameImpulseContracting ascending triangleContracting symmetrical triangle
Percent33.70.713.5
Table 19-2 Adjusted PercentagesCycle NameImpulseContracting ascending triangleContracting symmetrical triangle
Percent69.01.427.6
CAVEATAlthough a 69 percent probability is a rather respectabletrigger value when considering a possible market-entry order,the disadvantage is that the standard deviation is very high whenbasing the forecast solely on the two preceding wave heights.However, methods are presented in later chapters to lower thestandard deviation and improve the level of confidence. (Suchmethods involve basing the forecast on more than just twopreceding waves.)
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7
PARTFour-WaveCycles
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Chapter
20
Names ofMultiwaveCyclesOVERVIEWIn earlier chapters we indicated that the basic cycle consists ofthree consecutive waves and is identifiable by a single unique letterbetween “A” and “I” or “a” and “i” using the three logical operators , , and  . In this chapter we will introduce a method fornaming cycles with four or more waves.
OVERLAPPING WAVESWhen analyzing cycles consisting of more than three waves, wehave devised a naming convention that uses an overlapping-wavetechnique (Figure 20-1).For example, the four-wave cycle in this figure can be decomposed into the two overlapping three-wave cycles, as shown inFigure 20-2.Wave 2–3 on the left aligns perfectly with the wave 2–3 onthe right. The same is true for the waves 3–4 on the left and theright. The three-wave cycle on the left is a bull impulse cycle
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Part 7: Four-Wave Cycles
Figure 20-1 Basic Four-Wave Cycle.
(designated “A”), whereas the three-wave cycle on the right is abear connector cycle (designated “i”). Thus, in our namingscheme, the four-wave cycle in Figure 20-1 is labeled “Ai.”This naming convention can be extended indefinitely by addinga new letter to the current cycle name each time a new wave isappended. In the next example (Figure 20-3), a six-wave cycle is“decomposed” and labeled.The individual three-wave components are listed in Table 20-1.Thus the six-wave cycle in Figure 20-3 is identified as an “AiFa”cycle pattern.Note that the first and second waves of the rightmost cycle areoverlaid exactly on the second and third waves in the leftmostcycle. Both the heights (y axis) and the widths (x axis) of the twoshared waves must align perfectly to form a new wave cycle.
Figure 20-2 Components of a Four-Wave Cycle.
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Names of Multiwave Cycles
Figure 20-3 Six-Wave Cycle.
NAMING CONVENTIONIt is obvious that the four-wave cycle in Figure 20-1 is actually theconcatenation (or partial merging) of a three-wave bull impulsecycle and a three-wave bear connector cycle. Our labeling convention to identify the new four-wave cycle is “Ai.”Because of the constraints imposed by the three logical operators (, , and ) between adjacent waves, each three-wave cyclemay be merged only with three of the nine possible three-wavecycles. For example, the bull impulse cycle can only be overlappedwith a bear connector, a bear expanding ascending triangle, or abear expanding symmetrical triangle. These are the three cyclesin which the height of the second wave is always greater than theheight of the first wave.To further clarify the naming convention for four-wave cycles,we present one more example (Figure 20-4).
Table 20-1 Component WavesComponents
Cycle Name
Cycle ID
1–2–3–42–3–4–53–4–5–6
Bull impulseBear connectorBull contractingsymmetrical triangleBear impulse
AiF
4–5–6–7
a
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Part 7: Four-Wave Cycles
Figure 20-4 Four-Wave Bear Cycle.
The three waves on the left in Figure 20-4 form a bear contracting symmetrical triangle, whereas the three waves on the right forma bull impulse cycle. Thus the four-wave cycle in Figure 20-4 isdesignated as “eA.”
Chapter
21
Properties ofFour-WaveCyclesOVERVIEWUsing the same logical height relationship that was applied tothree-wave cycles, there are 27 possible four-wave patterns(3  3  3  27).
FREQUENCIESTable 21-1 is a frequency table that is sorted in descending orderby 25-pip reversal amount.Interesting to note in this table is the sharp decline in frequencybeginning with the cycle “FI.” All cycles above “FI” only use the“greater than” or the “less than” relationship.
FORECASTING THE FOURTH WAVEGiven any three-wave cycle, we can estimate the relationshipbetween the third and fourth waves using Table 21-2.In the next example (Figure 21-1), we will assume that a 15-pipswing reversal amount was used to create the swing data being scrutinized and that the last three-wave cycle was a bull connector cycle.133Copyright © 2007 by The McGraw-Hill Companies. Click here for terms of use.
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Part 7: Four-Wave Cycles
Table 21-1 Four-Wave Cycles Sorted by25-Pip ReversalCycle
5-Pip
15-Pip
25-Pip
IAAIHIAHIEEAHHEEFIDFIDAGGFCAFHEDGCDCHGCEDBBFGBBBBCCDFG
6.846.765.073.475.003.450.820.857.036.547.013.111.523.052.602.624.051.531.011.075.024.971.945.841.993.463.39
18.1618.6910.399.4610.8910.082.873.232.202.412.221.330.811.241.241.160.850.740.320.340.370.350.110.140.130.140.13
19.7318.9312.5912.2811.8711.644.273.780.790.720.720.570.420.420.380.260.230.230.080.040.040.040.000.000.000.000.00
The three possible continuations for the overlapping cycle area contracting symmetrical bear cycle (ID 