shifts in ftindamentals, such as the building of additional storage, will allow farmers to change their selling habits slightly. The right dsy to buy or sell in 1975 is not likely to be the right dsy this year. Even weekly data may be a litde too specific. Seasonal pattems are best seen using monthly data. The most we might expect is to know that the seasonal high in com usually occurs in July but sometimes in June or August; the harvest lows are likely in September but could be in October or November. We must first be aware of the big picture, then study how the specific pattem develops eadi year.

Recognizing Nonseasonal Years and External Factors

The studies of bull and bear martlet years shown in this book should make it clear that seasonality is not at all consistent. It is only a few years that cause prices to show extreme highs during the summer, while there are years in which the patterns are influenced by external factors and do not show normal seasonality. Seasonality, although a clear concept and a fad of nature, is not a trivial analjsis when spplied to trading. Eadi year must be observed and categorized, then a reasonable trading plan must be defined for that situation.

8 Cycle Analysis

The cycle is another basic element of price movement, along with the trend and seasonality, but it is more difficult to evaluate; therefore, it is often overlooked. Cjcles come in many forms-seasonality, production startup and shutdown, inventory - or stocks, behavioral, and astronomical. Seasonality is a special case of a calendar or annual cycle. Seasonality was covered in the previous chter and its special features are not considered here. Some of the cycles are clearly periodic, having regular intervals between peaks and vallejs; others are more uniform in their amplitude or height but irregular in period. The most definitive and regular cycle remains the seasonal, which is determined by periodic physical phenomena.

This chapter will discuss the major commodity cycles that result from business decisions, govemment programs, long-term market characteristics, and phenomena. Short-term cycles are usually atfributed to behavior and will be covered in a later chapter on pattem recognition. There are a few important wajs to find the cycle, the mosl common being trigonomefric curve fitting and Fourier (specfral) analjsis. Both will require a computer and will be explained in the following sections. Examples of solutions will he included in the explanation of the methods and applications will follow. Computer programs that solve the frigonomefric problems can be found in Appendix 4 along with additional examples,

CYCLE BASICS

Even when the seasonal pattem is eliminated, most cycles are still based on the periodic effects in our solar sjstem. After the I-year orbit of our planet around the sun. there is the 28-day lunar cycle; converted to business dajs. this gives the very familiar 20-day reference, which remains overwhelmingly popular among all analjsis. Other planetarj effects, which should by no means be discarded offhand, can be found in Chapter 14 under the topic "Financial Asfrologj" Throughout this chapter, there should be the undercurrent that planetarj motion may account for the consistency of any cycle that repeats with a fixed period.

Cjcles can be complex and difficult to see because there are often laier and smaller pattems, and cycles within cycles, all acting at the same time. Nevertheless, they exist and they are real. The cycles that appear to be most important are either long-term or the sum of a number of sii)cycles that come together at peaks or bottoms. This gives us a way to identifj one point on a cycle; we must remember that, when the individual components are found, there may be a number of smaller pattems that cause this effect. A reference to harmonics, just as in music, means that a smaller cycle is a fraction of the larger (for example, its cycle length is 1/2 K„ 1/4.... of the larger). When two cycles are sjnchronized. their peaks or vallejs occur at the same time. Any price series can be decomposed into individual cycles, although there may be many cycles needed.

Observing the Cjcle

Before selecting a maiket for cycle analjsis, it is necessarj to observe that a dominant Cjcle exists; it is also useful to know why it exists to avoid uncovering spurious pattems. This is

most easily done for markets in which you can clearly identifj the ftindamental and/or indusfrial reasons for cycles The basis for a cycle could be a pattem of holding inventory, the fixed time needed for breeding and feeding of livestock, seasonality or other economic factors. Figure 8-1 shows a clear 9- to 1 1-month cycle in live cattle ftitures prices over a past 6-year period. The peaks and vallejs varj by up to 1 month, making the pattem reli. able for use as part of a long-term frading sfrategj.

The Swiss franc cycle demonsfrated in Figure 8-2 is quite different. It ranges fran 24 to 35 weeks with a 40% variance compared with 20°o for cattle. Most important, the cycle in the Swiss franc cannot be related to any specific fundamental reason. Given enough variance, a repeating pattern can be found in any data. To rationally frade a cyclic pattem, there must be a reason for its existence and the confidence that it should continue.

A simple way to begin the search for major cycles is to look at a long-term chart, displayed as weekly rather than daily prices. The dominant half-cycle can be found by locating the obvious price peaks and vallejs, then averaging the distance between them. A convenient tool for estimating the cycle length is the Ehrlich Cjcle Finder. 3 It is an expanding device with evenly spaced points, allowing you to align the peaks and vallejs to observe the consistency in the cycle. For finding a single pattem, it is just as good as some of the mathematical methods that follow. It is best to have at least eight cycle repetitions before concluding that you have a valid cycle.

Cjcles can be obscured by other price patterns. A sfrong frend, such as the one in Swiss francs (Figure 8-2) or the seasonal movement of crops, may overwhelm a less pronounced cycle. Proper cycle identification requires that

these factors first be removed by deU-ending and by deseasonahzing. The resulting data will then be analyzed and the trend and seasonal factors added bad; once the cycle has been found. To find a subcycle, the primarj cycle should be removed and a second cycle analjsis performed on the data. The methods that follow (trigonomeUic regression and spectral analjsis) locate the dominant cycles at one time using integrated processes

The Kondratieff Wave

Much of the popularity of cycles is due to the publicity of Nicolai Kondratieffs 54-year cycle, known as the K-wave. During its documented span from about 1780 to the present, it appears to be very regular, moving from highs to lows and back again. In Figure 8-3 the Kondratieff wave is shown with the Wholesale Price Index as a measure of economic health .4 With only three full cycles completed, it is difficult to tell if the overall frend is moving upward or whether the entire pattem is just a coincidence

The forecast of the K-wave, shown in Figure 8-3, indicates a sha decline in wholesale prices due at about the year 1990, the milleniums equivalent to the depression of the 1930s. In fact, the early 1990s have posted remariable gains in the stock martlet, and at the end of the 1990s there is talk of disinflation fran the U.S. Federal Reserve; this may serve as some support for a continued cycle. Although interesting, a cycle of this length is impractical other than to point out that the peaks and valleys could varj by as much as 10" from the predicted values without diiriinishing the validity of the theory For the Kondratieff wave, a shift of 10° o, as seen in the 1930s, would cause a trading signal to buy 5 years too soon or too late. Determining cycles for any market has the same problem-the actual

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E 111 Meat and Livestock Markets,- in Tra.liiis Tactics

Jacob Beni.-tein, The Han.lt.O"k"fOiumodity?7cles iJ-Lii Wiley & Sons, New 19 1 Eliih cL vcle Fin.ler Jupany, 2220 W .yes street, Evanston, IL 60201 ilffinttM.lMtK-velrt" t»*..ical An . ..f Lt-cVs & O.niiuodities .July 1 -J)