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58 Ehierss objective is to find very shortterm cycles. By definition, these cycles must be the result of human behavior, rather than based on martlet economics, because fundamentals are not usually relevant to periods of only a few dajs, and they are not likely to have a regular pattem when they make a rare appearance. If very shortterm cycles exist, Qjiin, Entr.TV Meti,od( EMi." ! AuBlysis ..f & O.JijmoditieE (Febmsrv 19 Jee tile bitJiograrJiV LJiiiE Ehiers. "Hw to Use M.cimum Entr.f.y " TeeliuicBl AualysiE & Cjiimodities illoveniber ireii J.J,„ EEliierr.lJEcA and Trading M.iiket .?7cleE (JLii Wiley & ?i,E.New .* l99j. FIGURE 813 The phase angle forms a sawtooth pattem. Source: Jolm Ehiers, "Cjcle Analjsis and Intraday Trading Technical Analjsis of Stod & Commodities. II. no. 4 (February 1993). 1993 Technical Analjsis, Inc. Used with permission. they will not continue for long periods, and you must recognize them quickly if they are to be useful; therefore, shortterm cycles are found by analyzing only a small amount of recent data. Then how does it help to find a shortterm cycle based on a small amount of data, if it is not statistically dependable? In a lateral shift, Ehiers uses the existence of a shortterm cycle to tell if prices are in a sidewajs pattem or trending. If a shortterm cycle exists, then the maitet trend should be weak. Ehiers has no interest in trading the cycle, which is surprising for a cycle expert, but prefers the dependability of the trend. He has. instead, attempted to solve one of the most difficult problems facing the analjst. trjing to distinguish between a trending and sidewajs maiket. If a shortterm cycle exists, then we cannot rely on the trend. Ehiers develops this method throughout his book. CYCLE CHANNEL 1 ) A trendfollowing sjstem that operates for a maitet with a welldefined cyclic pattem should have specific qualities that do not necessarily exist in a generalized smoothing model. To confirm die cyclic turning points, which do not often occur precisely where they are expected, a standard moving average should be used, rather than an exponentially smoothed one. Although exponential smoothing alwajs includes some residual effect of older data, the determination of a cyclic tuming point must be limited to data that is nearer to onefourth of the period, combined with a measure of the relative noise in the series, which may obscure the turn. These features have been combined by Lambert" into a Commodity Cjcle Index ( ), which is calculated as follows: "Donald R. Lambert, "Commodity Channel Index Tools for Trading Cjclic Trends," Commodities (1980), reprinted in Technical Anahsis of Stocks & Commodities.
.015MD where x, = {fi, + Lj + Q/3 is the average of the daily high. low. and close x,= X Xi IS the moving average over the past days MD= X liJfl is the mean de\iation over the pastVdavs N is the number of days selected (less than c\clel Because all terms are divided by N, that value has been omitted. In the CCI calculations, the use of .0 I 5MD as a divisor scales the result so that 70° to 80° of the values fall within a +100 to 100 channel. The rules for using the CCI state that a value greater than +100 indicates a cyclic turn upward; a value lower than lOO defines a turn downward. Improvements in timing rest in the selection of N as short as possible but with a mean deviation calculation that is a consistent representation of the noise. The CCI concept of identifjing cyclic tums is good because of the substantial latitude in ttie variance of peaks and valleys, even with regular cycles. PHASING One of the most interesting applications of the cyclic element of a time series is presented by J.M. Hurst in The Profit Magic of Stock Transaction Timing (PrenticeHall): it is the phasing or sjnchronization of a moving average to represent cycles. This section will highlight some of the concepts and present a simplified example of the method. It is alreadj loiown that to isolate the cycle from the other elements, the frending and seasonal factors should be subtracted, reducing the resulting series to its cyclic and chance parts. In many cases, the seasonal and cyclic components are similar, but the frend is unique. Hurst freats the cyclic component as the dominant component of price movement and uses a moving average in a unique way to identifj the combined frendcycle. The sjstem can be visualized as measuring the oscillation about a straightline approximation of the frend (centered line), anticipating equal moves above and below. Prices have many long and shortterm frends, depending on the interval of analjsis. Because this technique was originally applied to sto(±s, most of the examples used by Hurst are longterm frends expressed in weeks. For commodities the same technique could be used b„ appljing the nearesl futures contract on a continuous basis As a simple example of the concept, choose a moving average of medium length for the frending component. The fullapan moving average may be selected by, averaging the distance between the tops on a price chart. The halfspan moving average is then equal to half the dsjs used in the fullspan average. The problem with using moving averages is that they awajs lag. A 40dsy moving average is alwajs 20 dsjs behmd the price movement. The current average is plotted under the most recent price, although it actually, represents the price pattem if the plot were lagged by onehalf the value of the average. This method applies a process called phasing, which aligns the tops and bottoms of the moving average with the corresponding tops and bottoms of the price movement. To phase the full and halfspan moving averages. lag each plot by half the dsjs in the average; this causes the curve to overlay, the prices (Figure 814). Then project the phased fulland halfapan moving averages until they cross. A line or curve connecting two or more of the most recent intersections will be the major frendline. The more points used, the more complicated the regression formula for calculating the trend; Chapter 3 discusses a variety of linear and nonlinear techniques for finding the best fit for these intersections Once the frendline is calculated, it is projected as the center of the next price cycle. With the frend identified and projected, the next step is to refiect the cycle about the frend. When the phased halfspan average turns down at point A (Figure 815), measure the greatest distance D of the actual prices above the projected frendline. The sjstem then anticipates the actual price crossing the frendline at point X and declining an equal distance D below the projected frendline. Once the projected crossing becomes an actual crossing, the distance D can be measured exactly and the price objective firmed. Rules for using this technique can be listed as follows:
1. Calculate the fullspan moving average for the selected number of days; lag the plot by half the days If the full span moving average uses F days, the value of the average is calculated at  F/2, where t is the current d. Call this phased point PH.. 2. The halfspan moving average is calculated for H days and plotted at /  H/2 + PH,. 3. Record the points where the two phased averages ¹, and PF, cross and call these pomVsX.„X„.u . . • 4. Find the trend by performing a linear regression on the crossing points X„. X„ Ifa straight line, then = HfcJtr FIGURE 814 Phasing. FIGURE 815 Finding the ti 5. Record the highest (or lowest) values of the price since the last crossing, 6. Calculate the projection of the halfspan by creating a straight line from the highest (or lowest, halfspan value since the last crossing ( ) to the last calculated halfspan value. This equation will beYc = c + dX. 7. Find the point at v \c\ the projected trendline cTO.sses the projected cyclic line by setting the equations equal to one another and solving totX and At the point of crossing {Xr, Kt) {X , , ing two equations in two unknowns, nich is easily solvable (X is time in days; Y is price). 8. If the halfspan is moving down, the maximum price reached by the commodity since the i: t crossmg IS subtracted from the Y coordinate of the projected crossing. This distance D is subfracted again from the Y
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