the first type of variation.Notice in the bull market example (Figures 13.13 and 13.14) thatthe top of wave B exceeds the top of A and that wave C violatesthe bottom of A.
Another variation occurs when wave B reaches the top of A,but wave C fails to reach the bottom of A. Naturally, this last pat-tern denotes greater market strength in a bull market. This varia-tion is shown in Figures 13.17-13.20 for bull and bear markets.Elliott Wave Theory
A Cc
Figure 13.9 Bull Market Flat (3-3-5), Normal Correction. (Frost andPrechter, p. 38. Copyright © 1978 byFrost and Prechter.)
Figure 13.11 Bear Market Flat(3-3-5), Normal Correction. (Frostand Prechter, p. 38. Copyright ©1978 by Frost and Prechter.)
327
A ¢c
Figure 13.10 Bull Market Flat (3-3-5), Normal Correction. (Frost andPrechter, p. 38. Copyright © 1978 byFrost and Prechter.)
Figure 13.12 Bear Market Flat (3-3-5), Normal Correction. (Frost andPrechter, p. 38. Copyright © 1978 byFrost and Prechter.)328
Chapter 13
8 8A Ac c
Figure 13.13 Bull Market Flat (3-3-5), Irregular Correction. (Frost andPrechter,p. 39. Copyright © 1978 byFrost and Prechter.)
Figure 13.15 = Bear Market Flat(3-3-5), Irregular Correction. (Frostand Prechter, p. 39. Copyright ©1978 by Frost and Prechter.)
Figure 13.14 Bull Market Flat (3-3-5), Irregular Correction. (Frost andPrechter, p. 39. Copyright © 1918 byFrost and Prechter.)
Figure 13.16 Bear Market Flat (3-3-5), Irregular Correction. (Frost andPrechter, p. 39. Copyright © 1978 byFrost and Prechter.)Elliott Wave Theory 329
 
A A
Figure 13.17 Bull Market Flat (3-_ Figure 13.18 Bull Market Flat
3-5), Inverted Irregular Correction.(Frost and Prechter, p. 40. Copyright© 1978 by Frost and Prechter.)
Figure 13.19 Bear Market Flat(3-3-5), Inverted Irregular Correction.(Frost and Prechter, p. 40. Copyright
(3-3-5), Inverted Irregular Correction.(Frost and Prechter, p. 40. Copyright© 1978 by Frost and Prechter.)
Figure 13.20 Bear Market Flat(3-3-5), Inverted Irregular Correction.(Frost and Prechter, p. 40. Copyright
© 1978 by Frost and Prechter.) © 1978 by Frost and Prechter.)
Triangles
Triangles usually occur in the fourth wave and precede the finalmove in the direction of the major trend. (They can also appearin the b wave of an a-b-c correction.) In an uptrend, therefore, itcan be said that triangles are both bullish and bearish. They’rebullish in the sense that they indicate resumption of the uptrend.They’re bearish because they also indicate that after one morewave up, prices will probably peak. (See Figure 13.21.)330 Chapter 13
BULL MARKET BEAR MARKET
ASCENDING (Top flat, bottom rising)
 
Figure 13.21 Corrective Wave (Horizontal) Triangles. (Frost andPrechter, p. 43. Copyright © 1978 by Frost and Prechter.)Elliott Wave Theory 331
 
Elliott’s interpretation of the triangle parallels the classicaluse of the pattern, but with his usual added precision. Rememberfrom Chapter 6 that the triangle is usually a continuation pattern,which is exactly what Elliott said. Elliott’s triangle is a sidewaysconsolidation pattern that breaks down into five waves, eachwave in turn having three waves of its own. Elliott also classifiesfour different kinds of triangles—ascending, descending, symmetri-cal, and expanding—all of which were seen in Chapter 6. Figure13.21 shows the four varieties in both uptrends and downtrends.
Because chart patterns in commodity futures contractssometimes don’t form as fully as they do in the stock market, it isnot unusual for triangles in the futures markets to have only threewaves instead of five. (Remember, however, that the minimumrequirement for a triangle is still four points—two upper and twolower—to allow the drawing of two converging trendlines.) ElliottWave Theory also holds that the fifth and last wave within the tri-angle sometimes breaks its trendline, giving a false signal, beforebeginning its “thrust” in the original direction.
Elliott’s measurement for the fifth and final wave aftercompletion of the triangle is essentially the same as in classicalcharting—that is, the market is expected to move the distancethat matches the widest part of the triangle (its height). There isanother point worth noting here concerning the timing of thefinal top or bottom. According to Prechter, the apex of the trian-gle (the point where the two converging trendlines meet) oftenmarks the timing for the completion of the final fifth wave.
THE RULE OF ALTERNATION
In its more general application, this rule or principle holds thatthe market usually doesn’t act the same way two times in a row.If a certain type of top or bottom occurred the last time around,it will probably not do so again this time. The rule of alternationdoesn’t tell us exactly what will happen, but tells us what proba-bly won’t. In its more specific application, it is most generallyused to tell us what type of corrective pattern to expect.Corrective patterns tend to alternate. In other words, if corrective332 Chapter 13
wave 2 was a simple a-b-c pattern, wave 4 will probably be a com-plex pattern, such as a triangle. Conversely, if wave 2 is complex,wave 4 will probably be simple. Figure 13.22 gives some examples.
 
Figure 13.22 The Rule of Alternation. (Frost and Prechter, p. SO.Copyright © 1978 by Frost and Prechter.)
CHANNELING
Another important aspect of wave theory is the use of price chan-nels. You'll recall that we covered trend channeling in Chapter 4.Elliott used price channels as a method of arriving at price objec-tives and also to help confirm the completion of wave counts.Once an uptrend has been established, an initial trend channel isconstructed by drawing a basic up trendline along the bottoms ofwaves 1 and 2. A parallel channel line is then drawn over the topof wave 1 as shown in Figure 13.23. The entire uptrend will oftenstay within those two boundaries.
If wave 3 begins to accelerate to the point that it exceedsthe upper channel line, the lines have to be redrawn along thetop of wave 1 and the bottom of wave 2 as shown in Figure13.23. The final channel is drawn under the two correctivewaves—2 and 4—and usually above the top of wave 3 as shownin Figure 13.24. If wave 3 is unusually strong, or an extendedElliott Wave Theory 333
 
Figure 13.23Old and NewChannels. (Frostand Prechter, p.62. Copyright ©1978 by Frostand Prechter.)
 
Figure 13.24
Final Channel. (Frostand Prechter, p. 63.Copyright © 1978 byFrost and Prechter.)
 334 Chapter 13
wave, the upper line may have to be drawn over the top of wave1. The fifth wave should come close to the upper channel linebefore terminating. For the drawing of channel lines on longterm trends, it’s recommended that semilog charts be employedalong with arithmetic charts.
WAVE 4 AS A SUPPORT AREA
In concluding our discussion of wave formations and guidelines,one important point remains to be mentioned, and that is the sig-nificance of wave 4 as a support area in subsequent bear markets.Once five up waves have been completed and a bear trend hasbegun, that bear market will usually not move below the previousfourth wave of one lesser degree; that is, the last fourth wave thatwas formed during the previous bull advance. There are excep-tions to that rule, but usually the bottom of the fourth wave con-tains the bear market. This piece of information can prove veryuseful in arriving at a maximum downside price objective.
FIBONACCI NUMBERS AS THEBASIS OF THE WAVE PRINCIPLE
Elliott stated in Nature’s Law that the mathematical basis for hisWave Principle was a number sequence discovered by LeonardoFibonacci in the thirteenth century. That number sequence hasbecome identified with its discoverer and is commonly referred toas the Fibonacci numbers. The number sequence is 1, 1, 2, 3, 5, 8,13, 21, 34, 55, 89, 144, and so on to infinity.
The sequence has a number of interesting properties, notthe least of which is an almost constant relationship between thenumbers.
1. The sum of any two consecutive numbers equals the nexthigher number. For example, 3 and 5 equals 8, 5 and 8equals 13, and so on.
2. The ratio of any number to its next higher numberapproaches .618, after the first four numbers. For example,Elliott Wave Theory 335
 
1/1 is 1.00, 1/2 is .50, 2/3 is .67, 3/5 is .60, 5/8 is .625, 8/13is .615, 13/21 is .619, and so on. Notice how these earlyratio values fluctuate above and below .618 in narrowingamplitude. Also, notice the values of 1.00, .50, .67. We'llcomment further on these values when we talk more aboutratio analysis and percentage retracements.
3. The ratio of any number to its next lower number is approx-imately 1.618, or the inverse of .618. For example, 13/8 is1.625, 21/13 is 1.615, 34/21 is 1.619. The higher the numbersbecome, the closer they come to the values of .618 and 1.618.
4. The ratios of alternate numbers approach 2.618 or itsinverse, .382. For example, 13/34 is .382, 34/13 is 2.615.
FIBONACCI RATIOS ANDRETRACEMENTS
It was already stated that wave theory is comprised of threeaspects—wave form, ratio, and time. We’ve already discussedwave form, which is the most important of the three. Let’s talknow about the application of the Fibonacci ratios and retracements.These relationships can apply to both price and time, althoughthe former is considered to be the more reliable. We'll come backlater to the aspect of time.
First of all, a glance back at Figures 13.1 and 13.3 showsthat the basic wave form always breaks down into Fibonacci num-bers. One complete cycle comprises eight waves, five up and threedown—all Fibonacci numbers. Two further subdivisions will pro-duce 34 and 144 waves—also Fibonacci numbers. The mathemat-ical basis of the wave theory on the Fibonacci sequence, however,goes beyond just wave counting. There’s also the question of pro-portional relationships between the different waves. The follow-ing are among the most commonly used Fibonacci ratios:
1. One of the three impulse waves sometimes extends. Theother two are equal in time and magnitude. If wave 5extends, waves 1 and 3 should be about equal. If wave 3extends, waves 1 and 5 tend toward equality.336 Chapter 13
2. A minimum target for the top of wave 3 can be obtained bymultiplying the length of wave 1 by 1.618 and adding thattotal to the bottom of 2.
3. The top of wave 5 can be approximated by multiplyingwave 1 by 3.236 (2x1.618) and adding that value to thetop or bottom of wave 1 for maximum and minimumtargets.
4. Where waves 1 and 3 are about equal, and wave 5 is expect-ed to extend, a price objective can be obtained by measur-ing the distance from the bottom of wave 1 to the top ofwave 3, multiplying by 1.618, and adding the result to thebottom of 4.
5. For corrective waves, in a normal 5-3-5 zig-zag correction,wave Cc is often about equal to the length of wave a.
6. Another way to measure the possible length of wave c is tomultiply .618 by the length of wave a and subtract thatresult from the bottom of wave a.
7. In the case of a flat 3-3-5 correction, where the b wavereaches or exceeds the top of wave a, wave c will be about1.618 the length of a.
8. In a symmetrical triangle, each successive wave is related toits previous wave by about .618.
Fibonacci Percentage Retracements
The preceding ratios help to determine price objectives in bothimpulse and corrective waves. Another way to determine priceobjectives is by the use of percentage retracements. The most com-monly used numbers in retracement analysis are 61.8% (usuallyrounded off to 62%), 38%, and 50%. Remember from Chapter 4that markets usually retrace previous moves by certain predictablepercentages—the best known ones being 33%, 50%, and 67%.The Fibonacci sequence refines those numbers a bit further. In astrong trend, a minimum retracement is usually around 38%. In aweaker trend, the maximum percentage retracement is usually62%. (See Figures 13.25 and 13.26.) 
bzzer7e (TR1600) Treasury Bonds 1600
 
Monthly Bar Chart
 
 
Fibonacci Retracements
 
 
 
 
Figure 13.25 = The three horizontal lines show Fibonnaci retracement lev-els of 38%, 50%, and 62% measured from the 1981 bottom to the 1993peak in Treasury Bonds. The 1994 correction in bond prices stopped right atthe 38% retracement line.
 
bers0e3 (TR1600) Treasury Bonds 1600Monthly Bar Chart
i
 
 
 
Figure 13.26 The three Fibonacci percentage lines are measured from the1994 bottom in bond prices to the early 1996 top. Bond prices corrected tothe 62% line.338 Chapter 13
It was pointed out earlier, that the Fibonacci ratiosapproach .618 only after the first four numbers. The first threeratios are 1/1 (100%), 1/2 (50%), and 2/3 (66%). Many students ofElliott may be unaware that the famous 50% retracement is actu-ally a Fibonacci ratio, as is the two-thirds retracement. A completeretracement (100%) of a previous bull or bear market also shouldmark an important support or resistance area.
FIBONACCI TIME TARGETS
We haven’t said too much about the aspect of time in waveanalysis. Fibonacci time relationships exist. It’s just that they’reharder to predict and are considered by some Elliotticians to bethe least important of the three aspects of the theory. Fibonaccitime targets are found by counting forward from significant topsand bottoms. On a daily chart, the analyst counts forward thenumber of trading days from an important turning point withthe expectation that future tops or bottoms will occur onFibonacci days—that is, on the 13th, 21st, 34th, 55th, or 89thtrading day in the future. The same technique can be used onweekly, monthly, or even yearly charts. On the weekly chart, theanalyst picks a significant top or bottom and looks for weeklytime targets that fall on Fibonacci numbers. (See Figures 13.27and 13.28.)
COMBINING ALL THREE ASPECTSOF WAVE THEORY
The ideal situation occurs when wave form, ratio analysis, andtime targets come together. Suppose that a study of waves revealsthat a fifth wave has been completed, that wave 5 has gone 1.618times the distance from the bottom of wave 1 to the top of wave3, and that the time from the beginning of the trend has been 13weeks from a previous low and 34 weeks from a previous top.Suppose further that the fifth wave has lasted 21 days. Oddswould be pretty good that an important top was near. 
(TR1600) Treasury Bonds 1600
 
Monthly Bar|Chart
Fibonacci Time Targets
 
 
 
 
 
 
 
 
Figure 13.27 Fibonacci time targets measured in months from the 1981bottom in Treasury Bonds. It may be coincidence, but the last four Fibonaccitime targets (vertical bars) coincided with important turns in bond prices.
 
(“OWI X) Dow Industrials
 
Monthly Bar Chart
Fibonacci Tine Targets
 
 
 
 
 
 
 
 
Figure 13.28 Fibonacci time targets in months from the 1982 bottom inthe Dow. The last three vertical bars coincide with bear market years instocks—1987, 1990, and 1994. The 1987 peak was 13 years from the 1982bottom—a Fibonacci number.340 Chapter 13
A study of price charts in both stocks and futures marketsreveals a number of Fibonacci time relationships. Part of the prob-lem, however, is the variety of possible relationships. Fibonaccitime targets can be taken from top to top, top to bottom, bottomto bottom, and bottom to top. These relationships can always befound after the fact. It’s not always clear which of the possiblerelationships are relevant to the current trend.
ELLIOTT WAVE APPLIED TOSTOCKS VERSUS COMMODITIES
There are some differences in applying wave theory to stocks andcommodities. For example, wave 3 tends to extend in stocks andwave 5 in commodities. The unbreakable rule that wave 4 cannever overlap wave 1 in stocks is not as rigid in commodities.(Intraday penetrations can occur on futures charts.) Sometimescharts of the cash market in commodities give a clearer Elliott pat-tern than the futures market. The use of continuation charts incommodity futures markets also produces distortions that mayaffect long term Elliott patterns.
Possibly the most significant difference between the twoareas is that major bull markets in commodities can be “con-tained,” meaning that bull market highs do not always exceedprevious bull market highs. It is possible in commodity marketsfor a completed five wave bull trend to fall short of a previous bullmarket high. The major tops formed in many commodity marketsin the 1980 to 1981 period failed to exceed major tops formedseven and eight years earlier. As a final comparison between thetwo areas, it appears that the best Elliott patterns in commoditymarkets arise from breakouts from long term extended bases.
It is important to keep in mind that wave theory was origi-nally meant to be applied to the stock market averages. It doesn’twork as well in individual common stocks. It’s quite possible that itdoesn’t work that well in some of the more thinly traded futuresmarkets as well because mass psychology is one of the importantfoundations on which the theory rests. Gold, as an illustration, isan excellent vehicle for wave analysis because of its wide following.Elliott Wave Theory 341
SUMMARY AND CONCLUSIONS
Let’s briefly summarize the more important elements of wave the-ory and then try to put it into proper perspective.
1.
2.
11.
12.
13.14.
15.
16.
A complete bull market cycle is made up of eight waves,five up waves followed by three down waves.
A trend divides into five waves in the direction of the nextlonger trend.
. Corrections always take place in three waves.. The two types of simple corrections are zig-zags (5-3-5)
and flats (3-3-5).
. Triangles are usually fourth waves, and always precede the
final wave. Triangles can also be B corrective waves.
. Waves can be expanded into longer waves and subdivided
into shorter waves.
. Sometimes one of the impulse waves extends. The other
two should then be equal in time and magnitude.
. The Fibonacci sequence is the mathematical basis of the
Elliott Wave Theory.
. The number of waves follows the Fibonacci sequence.10.
Fibonacci ratios and retracements are used to determineprice objectives. The most common retracements are 62%,50%, and 38%,
The rule of alternation warns not to expect the same thingtwice in succession.
Bear markets should not fall below the bottom of the pre-vious fourth wave.
Wave 4 should not overlap wave 1 (not as rigid in futures).The Elliott Wave Theory is comprised of wave forms,ratios, and time, in that order of importance.
The theory was originally applied to stock market averagesand does not work as well on individual stocks.
The theory works best in those commodity markets withthe largest public following, such as gold.342 Chapter 13
17. The principal difference in commodities is the existenceof contained bull markets.
The Elliott Wave Principle builds on the more classicalapproaches, such as Dow Theory and traditional chart patterns.Most of those price patterns can be explained as part of the ElliottWave structure. It builds on the concept of “swing objectives” byusing Fibonacci ratio projections and percentage retracements.The Elliott Wave Principle takes all of these factors into consider-ation, but goes beyond them by giving them more order andincreased predictability.
Wave Theory Should Be Used inConjunction with Other Technical Tools
There are times when Elliott pictures are clear and other timeswhen they are not. Trying to force unclear market action into anElliott format, and ignoring other technical tools in the process, isa misuse of the theory. The key is to view Elliott Wave Theory as apartial answer to the puzzle of market forecasting. Using it in con-junction with all of the other technical theories in this book willincrease its value and improve your chances for success.
REFERENCE MATERIAL
Two of the best sources of information on Elliott Wave Theoryand the Fibonacci numbers are The Major Works of R.N. Elliott,(Prechter, Jr.) and the Elliott Wave Principle (Frost and Prechter). Allof the diagrams used in Figures 13.1-13.24 are from the ElliottWave Principle and are reproduced in this chapter through thecourtesy of New Classics Library.
A primer booklet on the Fibonacci numbers, UnderstandingFibonacci Numbers by Edward D. Dobson, is available from TradersPress (P.O. Box 6206, Greenville, $.C. 29606 (800-927-8222). 
INTRODUCTION
Our main focus up to this point has been on price movement, andnot too much has been said about the importance of time in solv-ing the forecasting puzzle. The question of time has been presentby implication throughout our entire coverage of technical analy-sis, but has generally been relegated to secondary consideration.In this chapter, we’re going to view the problem of forecastingthrough the eyes of cyclic analysts who believe that time cycleshold the ultimate key to understanding why markets move up ordown. In the process, we're going to add the important dimen-sion of time to our growing list of analytical tools. Instead of justasking ourselves which way and how far a market will go, we'll startasking when it will arrive there or even when the move will begin.
Consider the standard daily bar chart. The vertical axisgives the price scale. But that’s only half of the relevant data. Thehorizontal scale gives the time horizon. Therefore, the bar chart isreally a time and price chart. Yet, many traders concentrate solelyon price data to the exclusion of time considerations. When we
343344 Chapter 14
study chart patterns, we’re aware that there is a relationshipbetween the amount of time it takes for those patterns to formand the potential for subsequent market moves. The longer atrendline or a support or resistance level remains in effect, themore valid it becomes. Moving averages require input as to theproper time period to use. Even oscillators require some decisionas to how many days to measure. In the previous chapter, we con-sidered the usefulness of Fibonacci time targets.
It seems clear then that all phases of technical analysisdepend to some extent on time considerations. Yet those consider-ations are not really applied in a consistent and dependable man-ner. That’s where time cycles come into play. Instead of playing asecondary or supporting role in market movement, cyclic analystshold that time cycles are the determining factor in bull and bearmarkets. Not only is time the dominant factor, but all other tech-nical tools can be improved by incorporating cycles. Moving aver-ages and oscillators, for example, can be optimized by tying themto dominant cycles. Trendline analysis can be made more precisewith cyclic analysis by determining which are valid trendlines andwhich are not. Price pattern analysis can be enhanced if combinedwith cyclic peaks and troughs. By the use of “time windows,” pricemovement can be filtered in such a way that extraneous action canbe ignored and primary emphasis placed only on such times whenimportant cycle tops and bottoms are due to occur.
CYCLES
The most intriguing book I’ve ever read on the subject of cycleswas written by Edward R. Dewey, one of the pioneers of cyclicanalysis, with Og Mandino entitled Cycles: The Mysterious ForcesThat Trigger Events. Thousands of seemingly unrelated cycles wereisolated spanning hundreds and, in some cases, thousands ofyears. Everything from the 9.6 year cycle in Atlantic salmon abun-dance to the 22.20 year cycle in international battles from 1415to 1930 was tracked. An average cycle of sunspot activity since1527 was found to be 11.11 years. Several economic cycles,including the 18.33 year cycle in real estate activity and a 9.2 yearstock market cycle, were presented. (See Figures 14.1 and 14.2.)345
Time Cycles
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Two startling conclusions are discussed by Dewey. First,that many of the cycles of seemingly unrelated phenomena clus-tered around similar periods. On p. 188 of his book, Dewey listed37 different examples of the 9.6 year cycle, including caterpillarabundance in New Jersey, coyote abundance in Canada, wheatacreage in the U.S., and cotton prices in the U.S. Why should suchunrelated activities show the same cycles?
The second discovery was that these similar cycles acted insynchrony, that is, they turned at the same time. Figure 14.3
THE 18.2-YEAR CYCLES ON PARADESree e e r e HPO PPT ERT TI TREE Or TOT
A Marriages, USA7  1869-70—1950-51v v“ / Flood Stages, NileMw SU’ 641-1451
“~ “ “sales of an Industrial Co.SY NU7 1872-1939
7¢_ Stock Prices70 1831 NODDY 1831-19644/ ImmigrationTo 1820 NT ODDS 1820-1962a “A “Construction, HamburgOe 7 1885-1935
“Real Estate ActivityTO 1881 NT DON N15 1° 1954
“A Public Utility Company
1903-1939
< Real Estate Transfer\Vf 1795-1958Residential BuildingJ --Nf wos 777 Construction° 1856-1950oA. Ru TeingConstruction1830-1936To 1514 * vl sf Java Tree Rings\U/ (Inverted)1814-1929
reiiecleiieiiiladisiielienalauialaaiieliiiliiaalaidaibsasatislrcusiih1880 1900 1920 1940 1960 1980
To 1795
 
Figure 14.3. The 18.2 year cycles on parade. (Source: Dewey, Edward R.,Cycles: The Mysterious Forces That Trigger Events (New York: ManorBooks, 1973.)348 Chapter 14
 
shows 12 different examples of the 18.2 year cycle including mar-riages, immigration, and stock prices in the U.S. Dewey’s startlingconclusion was that something “out there” in the universe mustbe causing these cycles; that there seemed to be a sort