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 TABLE 7-12 (Continued)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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el= 3 ss 5SS sjei./s/8//e/ale]/s]/sisle}s)eie}/2i al] a] 4g)s/elefelelsysefslsls/s/efslsjs|s/s/ eisS/S 3 . : 22/3) 2)2/35/8) 2/2) 51218) 2 12/3] S18] eis Ff) S| a) 329 | 63 75 | a7 | 86 |35 7 | 70 63 66 75 6 28LC 27 [18 | 27 6 30 235 66 [75 35 [33 69 | 64135 63 63172] 81 711 69 | 69 | 6670 66 | 91 | 75 | 63 15 64 | 6335 2 33 70 [35 | 37 18 | 37 729 [33 | 62172 [35 36 | 25 66 64 | 64 | 70 | 68 21 | 7_| 28 | 72 | 2870 | 66 72 30 [35 1631 64 | 29 | 37 | 36 | 36 | 33 33 37 [35/31 3312/16 27_| 37 | 36 | 80 | 75 83 [72 35 [35 [69 302 66 | 33 70 7 15 35 [3570 75 | 36 | 36 36[737 [37 36 66 | 66 | 66 | 72 el 3333 [37 63 | 63 _t 7076 | 7 63 | 66175 27 29 [26307 33 36 [72 72 [80 msl {68 7 3017 [35 [3335 22 66 | 63 7 70 35 | 33 3535 36 7 | 72) 72] 70 | | 66 [23 2566 36 | 35 37 | 31 | 35 | 69 28 | 83| 14A 64 29 29 78 | 33 | 8333.133 36 | 36 33 70. 37 66 35__ [35 33 | 36 wimt 7 75 | 69. 75 | 6435 | 27 29 36 3335 36 | 64 mi66 36 6 37 | 30 35ZI 29 “ttt 35] | 72 15 35 286 36 | 63 66 76 t 2 66 {7136 64 C70 Te [| [66 [80 | L 2822 66 | 63 | 37 37 zl66 66 | 27 36 | 64 | 64 37 6682 | 66 76 36 | 75 36 66]70 | 66 {T72 66 | 36 35 | 35 30 te36 63 | 33 | 63 | 35 | 35 37 25 {7 25 [2827 | 37 | 36 | 63 | 66 | 63.| 23 | 37 | 29 | 12 35/23] 2863 Bii 35{|__| [36/33] [ai 33 28— Te Bi | 66 | 7572 | 66 | 70 | 68 | 36 63 | 27 | 70 | 68 | 68 76 [66/721 64] 75] | 66 | 75 | 83 37 _t el | [28_ {7 90 | 66 | 75 | 3 | 63 | 64 | 64 66 | 66171 | 76 | 7163[e3| | C 7I70 72 | 70 a 63 | 66 35 | 35 | 35 | 37/35 | 84! 69 | 69 a"66 64 | 63 64 | 66 6464 72 | 75 [75 | 66 35 374 | 70 72 | 66 63 33 3066 | 33 72 | 83 | 83 | 75 | 63 | 64 35 69 | 76 [ 85 | 8333 35 63 76 66
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 188 SEASONALITY
 
COMMON SENSE AND SEASONALITYNonseasonal Markets ‘
Most comprehensive works on seasonality include not only agricultural markets but cur-rencies, interest rates, and indices. Common sense tells us that the primary feedgrains fol-low a clear seasonal pattern based upon a single crop year. This calendar cycle also appliesto coffee, cocoa, and oranges, although competition from South America has limited theextreme moves that resulted from a freeze in Florida’s orange groves. Grain seasonality hasbeen slowly changing as well, as Brazil improves their production of soybeans. Cattle andhog prices, dependent upon the cost of feed, and still marketed more actively in the fallbecause of weather, show a strong seasonal trend even though they have a growth andfeeding cycle that is not confined to a calendar year. Livestock patterns have adjusted tolong-term competition from Australia and New Zealand.
These agricultural markets are reasonable candidates for seasonal analysis, but mayrequire careful study to identify shifting patterns in competition and storage. What aboutTreasury bonds or the Japanese yen? Should we look for seasonal patterns in the financialmarkets? While we can argue that certain stocks are highly dependent upon seasonal busi-ness, can we say that the demand on money is higher in the summer than in the winter, orthat enough tourists convert their currencies to yen when they visit Japan during the sum-mer that this effect drives the value of the yen consistently higher? Are automobile exportsfrom Japan stronger or weaker during a certain season, so that there is a predictable pat-tern? These scenarios are highly unlikely and have no assurance, such as the coming ofwinter, that cars must be sold the way grain must be harvested. In financial markets theplayers can choose their time to act; they can hedge their commitments or wait for a bet-ter opportunity. This choice makes any pattern that might exist uncertain. The study of sea-sonality should be limited to those markets that depend on weather and seasons, eitherdirectly or indirectly.
Being Too Specific about Targets
Nature is not precise and selecting an optimal day of the year to set a long position is notlikely to work. Small shifts in fundamentals, such as the building of additional storage, willallow farmers to change their selling habits slightly. The right day to buy or sell in 1975 isnot likely to be the right day this year. Even weekly data may be a little too specific. Sea-sonal patterns are best seen using monthly data. The most we might expect is to know thatthe seasonal high in corn usually occurs in July but sometimes in June or August; the har-vest lows are likely in September but could be in October or November. We must first beaware of the big picture, then study how the specific pattern develops each year.
Recognizing Nonseasonal Years and External Factors
The studies of bull and bear market years shown in this book should make it clear that sea-sonality is not at all consistent. It is only a few years that cause prices to show extreme highsduring the summer, while there are years in which the patterns are influenced by externalfactors and do not show normal seasonality. Seasonality, although a clear concept and a factof nature, iS not a trivial analysis when applied to trading. Each year must be observed andcategorized, then a reasonable trading plan must be defined for that situation. 
Cycle Analysis
sonality, but it is more difficult to evaluate; therefore, it is often overlooked. Cycles
come in many forms—seasonality, production start-up and shutdown, inventory orstocks, behavioral, and astronomical. Seasonality is a special case of a calendar or annualcycle. Seasonality was covered in the previous chapter and its special features are not con-sidered here. Some of the cycles are clearly periodic, having regular intervals betweenpeaks and valleys; others are more uniform in their amplitude or height but irregular inperiod. The most definitive and regular cycle remains the seasonal, which is determined byperiodic physical phenomena. .
This chapter will discuss the major commodity cycles that result from business deci-sions, government programs, long-term market characteristics, and phenomena. Short-termcycles are usually attributed to behavior and will be covered in a later chapter on patternrecognition, There are a few important ways to find the cycle, the most common beingtrigonometric curve fitting and Fourier (spectral) analysis. Both will require a computerand will be explained in the following sections. Examples of solutions will be included inthe explanation of the methods and applications will follow. Computer programs that solvethe-trigonometric problems can be found in Appendix 4 along with additional examples.
T= cycle is another basic element of price movement, along with the trend and sea-
CYCLE BASICS
Even when the seasonal pattern is eliminated, most cycles are still based on the periodiceffects in our solar system. After the 1-year orbit of our planet around the sun, there is the28-day lunar cycle; converted to business days, this gives the very familiar 20-day reference,which remains overwhelmingly popular among all analysts. Other planetary effects, whichshould by no means be discarded offhand, can be found in Chapter 14 under the topic“Financial Astrology.” Throughout this chapter, there should be the undercurrent that plan-etary motion may account for the consistency of any cycle that repeats with a fixed period.
Cycles can be complex and difficult to see because there are often larger and smallerpatterns, and cycles within cycles, all acting at the same time. Nevertheless, they-exist andthey are real. The cycles that appear to be most important are either long-term or the sumof a number of subcycles that come together at peaks or bottoms. This gives us a way toidentify one point on a cycle; we must remember that, when the individual componentsare found, there may be a number of smaller patterns that cause this effect. A reference toharmonics, just as in music, means that a smaller cycle is a fraction of the larger (for exam-ple, its cycle length is 4, 4, 4, ... of the larger). When two cycles are synchronized, theirpeaks or valleys occur at the same time. Any price series can be decomposed into individ-ual cycles, although there may be many cycles needed.
Observing the Cycle
Before selecting a market for cycle analysis, it is necessary to observe that a dominant cycleexists; it is also useful to know why it exists to avoid uncovering spurious patterns. This is192 CYCLEANALYSIS
 
 
FIGURE 8-2 Cycles in Swiss franc futures.
 
Weekly High, Low—Friday Close ‘COMMOOITY PERSPECTIVE/CHICACO, RLINOFS Aono
 
 
 
SFUANIIAS ONO UFAAN JIA TONDUFHAM SIA SONOS FRAN SIATONOUFHANJIABOND UFR AN1978 1978 1977 3078 1979
 
Source: J. Bernstein, The Handbook of Commodity Cycles (New York: John Wiley & Sons, 1982).
price pattern will never correspond exactly to the predicted peaks and valleys, which,because they are a mathematical cycle, must come at regular intervals.
Terminology
Before getting very technical about the measurement and calculation of cycles, there are a.few terms that describe most of the concepts discussed throughout this chapter. Note thatthe use of wave and cycle is interchangeable.UNCOVERING THE C¥CLE 193_
FIGURE 8-3 The Kandratieff Wave.
The Kondratieff wave
 
Roaring 20s
 
 
 
 
 
US. Wholesaie prices
 
: 1800 1820 1840 1860 1880 1900 1920 1940 1960 198020 - ns
 
Source: Jeff Walker, “What K-wave?” Technical Analysis of Stocks & Commodities, 8, no. 7 (July 1989).© 1989Technical Analysis, Inc. Used with permission.
Amplitude—the height of the wave (cycle)Period—the time needed to finish one wave (one cycle)Frequency—(for the more mathematical) the number of cycles that repeat every 360°
Phase—a measurement of the separation of tops or bottoms of two waves with thesame period
Left and right translation—the tendency for a cycle peak to fall to the left or right ofthe center of the cycle
UNCOVERING THE CYCLE
Before resorting to the highly mathematical methods for finding cycles, there are somesimple approaches that may serve many traders. For example, if you believe that there is adominant 20-day cycle, then you simply create a new price series by subtracting the currentdata from a 20-day moving average. This removes the trend that may obscure the cycle.Most oscillators, such as a stochastic or RSI, also serve to identify a price cycle.
Enhancing the Cycle by Removing the Trerid_
The cycle can become more obvious by removing the price trend. The use of two trend-lines seems to work very well in most cases.” First, smooth the data using two exponentialmoving averages, in which the longer average is half the period of the dominant cycle(using your best guess), and the shorter one is half the period of the other. Then create an
>In his article, “Finding Cycles in Time Series Data” (7echnical Analysis of Stocks & Commodities (August 1990)),A. Bruce Johnson credits John Ehlers for his work in the use of two exponential trends. See John Ehlers, “MovingAverages, Part 1” and “Moving Averages, Part 2,” Technical Analysis of Stocks & Commodities (1988).194 CYCLE ANALYSIS
 
MACD index by subtracting the value of one exponential trend from the other; the result-ing synthetic series avoids the lag inherent in most methods.
A technique that enhances the cycle is the use of triangular weighting instead of expo-nential smoothing. This method creates a set of weighting factors that are smallest at theends and peak in the middle of the weighted average. For example, if you wanted a 10-period triangular average, the peak weighting factor would always be 2.0 and is assignedto the price just before the middle (there is no middle value for an even number of peri-ods; therefore, the first value is eliminated), then weighting factors would begin andincrease by 2.0/(P/2), where P = 10. This creates the series of weighting factors, beginningat t- P + 2 (to get a center value you need to have an odd number of entries), .4, .8, 1.2,1.6, 2.0, 1.6, 1.2, .8, .4. Once the weighting factors, w, are known, the sum of the weight-ing factors is P (the same as the period), and the triangular average is
TMA, = (W.X P, p22 + Wo XPrepag to + Wer X PY/P
When applying a triangular average, each of the two averages used (one of which is half theperiod of the other) get triangular weights and the difference is taken. The smooth curveof the triangular MACD in Figure 8-4 shows what appears to be a regular cyclic pattern inthe price of IBM.
Trigonometric Price Analysis
Most cycles can be found using the trigonometric functions sine and cosine. These func-tions are also called periodic waves, because they repeat every 360° or 2 radians (where %= 3.141592). Because radians can be converted to degrees using the relationship
2n1 degree = 360
all work that follows will be in degrees. Some other necessary terms are:
Amplitude (a)—the height of the wave from the center (x = axis)
Frequency (®)—the number of wavelengths that repeat every 360°, calculated as@=1/T
Period (T)—the number of time units necessary to complete one wavelerigth (cycle)
A simple sine wave fluctuates back and forth from +1 to -1 (0, +1, 0, -1, 0) for eachcycle (one wavelength) as the degrees increase from 0° to 360° (see Figure 8-5). To relatethe wavelength to a specific distance in boxes (on graph paper), simply divide 360° bythe number of boxes in a full wavelength, resulting in the box size (in degrees). Forexample, a 100-box cycle would give a value of 3.6° to each box. The wavelength can bechanged to other than 360° by using the frequency as a multiplier of the angle of the sinewave
sin @O
If @ > 1, the frequency increases and the wavelength shortens to less than 360°; if w <1, the frequency decreases and the wavelength increases. Because @ is the frequency, itgives the number of wavelengths in each 360° cycle. To change the phase of the wave (thestarting point), the value & is added to the angle
sin (@ + 6)
If b is 180°, the sine wave will start in the second half of the cycle; & serves to shift thewave to the left. The amp/litude can be changed by multiplying the resulting value by a con-UNCOVERING THE CYCLE 195
 
 
FIGURE 8-4 A triangular MACD shows an apparent cycle in IBM.
Johnson indicator on IBM 2/1/88-3/30/90,IBM 2/1/88-3/30/90
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