14-6 Jupiter and Saturn Planet RX and Stations, 1996-2001*
 
 
jupiter jupiter Soturn Saturn
(Retrograde) (Direct) (Retrograde) (Direct)1996 May 4 Sep 3 Jul 18 Dec 31997 Jun9 Oct 8 Aug | Dec 161998 Julie Nov 13 Aug 15 Dec 291999 ‘Aug 25 Dec 20 Aug 302000 Sep 29 . Sep 12 Jan 12 (Jupiter not in sequence)2001 Nov 2 Jan 25 Jan 24, Sep 26 (Saturn not in sequence)2002 Mari. Feb 8
fa*Source: Weingarten, Investing by the Stors.
aTABLE 14-7 Eclipses, 1996-2001* ~
 
 
Lunar Solar tunar Solar_ Eclipse Eclipse Eclipse ~ Eclipse1996 Apr 4 Apr (7 Sep 27 Oct 121997 Mar 24 Mar 9 Sep 16 Sep 21998 . Mar 13 Feb 26 Aug 8 Aug 22Sep 61999 Jan 31 Feb 16 Jul28 Aug (12000 jan 2l - Feb julle Jul |Jul 31 - Dec 25200! fan9 Jun 21 Jul s Dec |4Dec 30
i*Source: Weingarten, investing by the Stors.376 BEHAVIORAL TECHNIQUES
 
_—_—TABLE 14-8 New and Full Moons, Eclipses 1996~2001*
 
New Full New Full New Full ~New Full ~=New = Full «= New — Full
 
1996 JanS  Jan20 Feb4 FebI8 MarS Mar I9 Apr4 Apr l7 May3 May I7 Jun |Jun 16 Jull = JuliS Jul3Q Aug 14 Aug28 Sep 12 Sep 27 Oct 1l2 Oct 26 Nov tI Nov 25Dec 10 Dec 24
1997 Jan9  Jan23. Feb7 Feb 22 Mar9 Mar24 Apr7 Apr22 May6 May 22 JunS Jun 20Jul4 Jul20. Aug3) Aug 18 Sep! Sep 16 Oct} Oct !6 Nov 14 Nov 30 Dec 14 Dec 19
1998 Jan 2) Jan28 Feb I! Feb 26 Mar ‘3 Mar 28 April Apr 26 May Il May 25 Jun 10Jun 24 Jul9 — Jul23. Aug8 Aug 22 Sep9 Sep20 OctS Oct20 Nov4 Nov 19 Dec3Dec 18
1999 Jan2 Jan 17 Jan31 Feb 16 Mar2 Mar 17 Mar 3! Apr 16 Apr 30 May IS May 30Jun '3) Jun 28 Jult3  Jul28 Aug il Aug26 Sep9 Sep25 Oct9 Oct24 Nov 23 Dec7Dec 22
2000 Jan6 Jan2I FebS Feb 19 Maré Mar 20 Apr4 Aprl8 May4 May I8 Jun2 Jun l6Jull  Jul31 Aug 1S Aug 29 Sep 13 Sep27 Oct 13 Oct 27 Nov Il Nov25 Dec Il Dec 25
2001 Jan9° Jan24 Feb8 Feb23 Mar9 Mar 25 Apr8 Apr24 May7 May 23 Jun6Jun24 Jul5 = Jul20. Aug4 Aug l9 Sep2 Sep 17 Oct2 Oct 16 Novi Nov IS Nov 30Dec 14 Dec 30
 
*Source: Weingarten, Investing by the Stors.
swings, the more significant the results. By creating a table of key reversal levels, it may bepossible to find those aspects that exert the greatest influence on the market. Once iso-lated, they may be used as a bias within a technical program.
The Moon: Buy Full, Sell New
It is known that the moon’s effect on our planet is great—it is vitally connected with themovement of all fluids. The mass of the moon is about %: that of the Earth and larger thanthe planet Pluto. It is remarkably large for a moon, with a diameter of 3,476 kilometers,27% that of the Earth, Because of its large presence and close proximity to the Earth (about230,000 miles), the moon is also believed to affect human behavior in strange ways, espe-cially during a new or full moon. N
In an experiment conducted on an arbitrary set of futures markets for the year 1972,it was shown that short-term movements of prices react with some uniformity with respectto the phases of the moon, In fact, the markets chosen for observation—silver, wheat, cat-tle, cocoa, and sugar—showed an uncanny ability to form a rising market following a fullmoon and a falling market after a new moon.
To find the phases of the moon, you can refer to a number of books or any calendar;however, to perform any lengthy study of the moon's effect on prices, the moon’s phasesshould be computerized. An Easy Language function that gives the dates of the new andfull moon follow. .
Calculation of a New Moon, Full Moon, Solar and Lunar Eclipse
Although a highly accurate calculation of planetary positions and eclipses requires consid-eration of many minor items, a good approximation can be found with far less difficulty.”*
* Todd Lofton, “Moonlight Sonata,” Commodities uly 1974). -“1 Jean Meeus, Astoriomical Algorithms (Willmann-Bell, Inc., RO. Box 35025, Richmond, VA 23235, 1991, Chap-ter 52). Ashorter version appears in another volume, Astronomical Formulae for Calculators, Fourth Ed, (1988).For complete accuracy, the author refers readers to the Astronomical Almanac, or the Canon by Mucke andMeeus. The material in this section combines both versions of Meeus’s work.
  FINANCIAL ASTROLOGY 377
 
To calculate the exact time of the eclipses, it is first necessary to find the time of the newand full moons. The resulting times are expressed in Julian Ephemeris Days (JDE), alsocalled dynamic time (DT).
Lunar Phases
The new and full moons are simply two of the four lunar phases, measuring when theexcess of the apparent longitude of the moon over the apparent longitude of the Sun is 0°,90°, 180°, and 270°. The times of these phases are given by the Julian date:
1. JDE = 2451550.09765 + 29.530588853k + 0.0001337T?~ 0.0000001507°? + 0.000000000737*
where an integer value of & gives the new moon (i.e., 1, 2, 3,...), and an integervalue increased by .25, .50, or .75 (e.g., 1.25, 1.50, 1.75) gives the three quarters,respectively. The value & = 0 corresponds to the new moon of January 6, 2000. Neg-ative values indicate times prior to the year 2000. T is the time in Julian centuriessince 2000, found by T= k/1236.85. .
To check your results, k is approximately equal to (year — 2000) x 12.3685 andthe year is expressed in decimal (e.g., the end of March 1997 is 1987.25)
Using this formula, we can get a list of dates for the full moon from about 1995through the year 2000 (approximately 62) by creating an array called JDE and find-ing the 62 dates of the new and full moons ending at the year 2000 using theTradeStation code as shown in Figure 14-23.
For each value of & in the previous program, corrections must be made to findthe exact time of maximum solar or lunar eclipse using the following values:
2. Eccentricity of the Earth's orbit around the Sun:
£=1-0.002516T — 0.0000074773. The Sun’s mean anomaly at time JDE:M = 2.5534 + 29.10535669k — 0.00002 187? — 0.000000117?
—FIGURE 14-23 TradeStation function to calculate the moon’s phases, Results are in JEDand must be converted to calendar date.
 
{MOONPHASESReturns the mean phases of the moon, corrected for the sun’s aberration}VARS: k(O), t(0), next{O), 1(0);ARRAY fullmoon[62](0), newmoon[62](0);next = -62;for i = 1 to 62 begin =~ k = next; {newmoons relative to the year 2000}T= k / 1236.85; {time in Julian centuries}newmoon[i] = 2451550.09765 + 29.530588853*k+ 0.0001337*@power(T,2);-0.000000150*@power(T,3) + 0.00000000073*@power(T 4);k = next .5: {full moons relative to the year 2000}T=k / 1236.85;fullmoonli] = 2451550.09765 + 29.530588853*k+ 0.0001337*@power(T,2)-0.000000150*@power(T,3) + 0.00000000073*@power(T, 4);next = next + 1;end: 
 
378 BEHAVIORAL TECHNIQUES
4. The moon’s mean-anomaly:
M’ = 201.5643 + 385.81693528k + 0.010743877+ 0.000012397? — 0.0000000587*5. The moon’s argument of latitude:F= 160.7108 + 390.67050274k — 0.0016341T”— 0.000002277? + 0.0000000117*
6. The ascending node of the lunar orbit:
Q (Omega) = 124.7746 ~ 1.56375580k + 0.00206917? + 0.000002157?
7. The eccentricity of the Earth’s orbit around the Sun:
E=1-0.002516T — 0.00000747?
8. The following calculation, based on F and Q, gives the basis for the solar or lunareclipse; and if F differs from 0°, 180°, or 360° by less than 13°.9 then an eclipse iscertain. If F is more than 21° from these phases, there is no eclipse. ir F falls be-tween these values then there is no eclipse if |sin F| > .36.
The next components needed for corrections are:F, =F -0°.02665 sinQ= 299°.77 + 0°.107408k ~ 0.00917377
9. Then to find the exact time of the full solar (or lunar) eclipse, the following correc-tions (in days) should be added to the time of the mean conjunction given by JDEin the first formula above (smaller quantities have been omitted):
Time of maximum eclipse
= JDE + @unar or solar component below) XN
+ 0.0161 sin 2M’ — 0.0097 sin 2F, + 0.0073 x £ x sin (M’ - M)— 0.0050 x Ex sin (M’ + M) ~ 0.0023 sin (M’ - 2F,) + 0.0021 x Ex sin 2M+ 0.0012 sin (M’ + 2F,) + 0.0006 x £ x sin (2M’ + M) ~ 0.0004 sin 3M’~ 0.0003 x £ x sin (M + 2F,) + 0.0003 sin A; ~ 0.0002 x £ x sin (M — 2F,)~ 0.0002 x £ x sin (2M’ - M) ~ 0.0002Q
solar component = ~0.4075 sin M’ + 0.1721 x ExsinM
lunar component = —0.4065 sin M’ + 0.1727 x Ex sin M
10. P=0.2070 x E x sin M + 0.0024 x Ex sin 2M ~ 0.0392 sin M’ + 0.0116 sin 2M’
~ 0,0073 x E x sin (M’ + M) — 0.0067 x E x sin @M’ - M) + 0.0118 sin 2F,
11. Q =+5.2207 — 0.0048 x Ex cos M + 0.0020 x E x cos 2M ~ 0.3399 cos M’
— 0.0060 x E x cos (M’ + M) + 0.0041 x E x cos (M’ — My
12. W=| cos F, |
13. y (gamma) = (P cos F, + Q sin LF) x (1-0: 0048w)
14. u = 0,0059 + 0.0046 cos M— 0.0182 cos M’ + 0.0004 cos 2M’ — 0.0005 cos (M+ M’)FINANCIAL ASTROLOGY 379
 
Solar Eclipses
For a solar eclipse, 7 represents the shortest distance from the axis of the moon's shadowto the center of the Earth in units of the equatorial radius of the Earth (the distance fromthe center to the surface of the Earth at the equator). Its value is positive if the axis of theshadow is passing north of the Earth’s center, and negative if it is passing south. When y isless than +.9972 and greater than ~.9972, the solar eclipse is central; that is, there is a lineof central eclipse on the surface of the Earth (see Figure 14-24).
The value w gives the radius of the moon's umbral cone on the fundamental plane,which passes through the center of the Earth perpendicular to the axis of the moon’sshadow (in units of Earth's equatorial radius). The radius of the penumbral cone in thefundamental plane is u + 5460.
Based on these values, the following situations exist:
| y | is between 0.9972 and 1.5432+u The eclipse is not central.
| y | is between 0.9972 and 1.0260 Part of the eclipse may touch the polarregions.
0.9972 < | y¥|< 0.9972 + lal The combination of a noncentral total orannular eclipse.
| y | >1.5432+u , No eclipse is visible from the Earth’s sur-face.
For a central eclipse,
u<0 The eclipse is total.
u > 0.0047 - The eclipse is annular.
0<u<0.0047 : The eclipse is either.annular or annular-total.
To remove the ambiguity of this last situation, calculate@ = 0.00464 cos W where sin W=y
If uw < then the eclipse is annular-total; otherwise, it is annular.
 
FIGURE 14-24 Geometry ofa solar eclipse.
 
 380 BEHAVIORAL TECHNIQUES
 
The greatest magnitude for a partial solar eclipse is reached at the point on the Earth’ssurface that comes closest to the axis of the shadow at )
15433 +u— |y|
Greatest magnitude of solar eclipse = 0.5461 + 2u
Lunar Eclipses
For a lunar eclipse, y is the least distance for the center of the moon to the Earth’s shadow(see Figure 14-25). The value is positive if the moon's center is passing north of the axisof the shadow, and negative if it is passing south. At the distance of the moon, the penum-bra radius p = 1.2847 + u and the umbra radius 6 = 0.7404 —u. The magnitude of the lunareclipse is
penumbral eclipses: (1.5572 +u- | y |) / 0.5450umbral eclipses: (1.0129 ~u — | y |) /0.5450
If the magnitude is less than zero, there is no eclipse. The semidurations of the partial and.total phases in the unibra are calculated as
P=1.0129-uT= 0.4679 -un = 0.5458 + 0.0400 cos M’
and the semidurations in minutes are
partial phase = se (Pp? ~y?
total phase -2 VT -¥
Example: Solar eclipse of May 21, 1993:The following values can be used to verify your calculations:
May 21 is the 141st day of the year, therefore
k= 1993 + 141365 = 1993.38T = 1993.38/1236.85 = 1.6116.JDE = 2449128.5894
 
FIGURE 14-25 Geometry ofa lunar eclipse. ~
 FINANCIAL ASTRULOGY 381
 
M= 135°.9142 P =0.1842M = 244°.5757 OQ =5.3589F=165°.7296 y= 1.1348Q = 253°.0026 u = 0.0097
F,= 165°.7551
Because 180° ~ F is between 13°.9 and 12°.0 the eclipse is uncertain, and because | ¥ |is between 0.9972 and 1.5433 + u = 1.553, the eclipse is partial. By calculating the greatestmagnitude of a solar eclipse, we get 0.740. Because F is near 180°, the eclipse occurs nearthe moon’s descending node, and because ¥ is positive, the eclipse is visible in the northernhemisphere of the Earth. By adding the corrections to JDE, the final time of maximumeclipse is 2449129.0979, which corresponds to May 21, 1993, at 14h21m0s TD. This differsfrom the exact value of 14h20m14s TD by less than 1 minute.380 BEHAVIORAL TECHNIQUES
 
The greatest magnituUe for a partial solar eclipse is reached at the point on the Earth’ssurface that comes closest to the axis of the shadow at 1
1.5433 +u- |y|
Greatest magnitude of solar eclipse = 0.5461 4 2u
Lunar Eclipses
For a lunar eclipse, 7 is the least distance for the center of the moon to the Earth’s shadow(see Figure 14-25). The value 7 is positive if the moon’s center is passing north of the axisof the shadow, and negative if it is passing south. At the distance of the moon, the penum-bra radius p = 1.2847 + u and the umbra radius 6 = 0.7404 — u. The magnitude of the lunareclipse is
penumbral eclipses: (1.5572 +u—| y |) /0.5450umbral eclipses: (1.0129 ~ u~ | y |) /0.5450
if the magnitude is.less than zero, there is no eclipse. The semidurations of the partial andtotal phases in the wmbra are calculated as
P=1,0129-u 1T= 0.4679 -un= 0.5458 +'0.0400 cos M’
and the semidurations in minutes are
0partial phase = ° VP?-y
0total phase = o T-y
Example: Solar eclipse of May 21, 1993: _The following values can be used to verify your calculations:
May 21 is the 141st day of the year, therefore
R= 1993 + 141/365 = 1993.38T = 1993.38/1236.85 = 1.6116.JDE = 2449128.5894
 
FIGURE 14-25 Geometry ofa lunar eclipse.
 FINANCIAL ASTR. _OGY 381
 
M = 135°.9142 P=0.1842M’ =244°.5757 Q= 5.3589F=165°.7296 y= 1.1348Q = 253°.0026 u = 0.0097
F, = 165°.7551
Because 180° — F is between 13°.9 and 12°.0 the eclipse is uncertain, and because | ¥ |is between 0.9972 and 1.5433 + uw = 1.553, the eclipse is partial. By calculating the greatestmagnitude of a solar eclipse, we get 0.740. Because F is near 180°, the eclipse occurs nearthe moon’s descending node, and because 7 is positive, the eclipse is visible in the northernhemisphere of the Earth. By adding the corrections to JDE, the final time of maximumeclipse is 2449129.0979, which corresponds to May 21, 1993, at 14h21m0s TD. This differsfrom the exact value of 14h20m14s TD by less than 1 minute.| 15
Pattern Recognition
 
ditional charting, which is entirely the identification of common formations; even
moving averages attempt to isolate, using mathematical methods, what has been visu-ally determined to be a trend. Traders have always looked for patterns in price movement.Because they were not equipped with computers, their conclusions are considered marketlore rather than fact and are handed down from generation to generation as proverbs, suchas “Up on Monday, down on Tuesday,” “Locals even up on Fridays,” and “Watch for keyreversals.” Because these three sayings have endured, they are candidates for analysis laterin this chapter.'
’ The earliest technical systems based on patterns were of the form: “If after a sharp rise#he market fails to advance for 3 days, then sell.” As computers became more powerful,more complex approaches could be taken. For example, by observing the closing pricesstarting on an arbitrary day, a// patterns of higher and lower closes can be recorded to findtheir tendency to repeat. A computer is well-equipped to perform this task. First, the 2- and3-day patterns are eliminated because the recurrence of up-down or down-up and theequivalent 3-day patterns would be too frequent to be meaningful. Then, the closing pricesare scanned for occurrences of predefined patterns. For example, if an up-up-down-up-down-up is to be matched, every six consecutive prices must be tested. From a table ofoccurrences we can conclude that these patterns can be predicted in advance or that theyare leading indicators of other price moves. This approach, as well as the combination ofevents used to forecast profitable situations, are discussed later in this chapter.
Pattern recognition may appear to be more of a game than a business, but it is a sourceof many valuable ideas. Figure 15-1, a graph of the New York Stock Exchange (1854-1959),shows the simplification of patterns to the point where it is difficult not to count the recur-rences of the more obvious patterns and look for the formations that precede them to seewhether they could be predictive. For example, in 1922, 1924, and 1927, there were sharpadvances in the market; the years preceding those showed an identical U pattern. It wouldbe interesting to see whether another occurrence of a symmetric U was followed by a sim-ilar rise. Another pattern that stands out is that of two consecutive years of sharp rise,1862-1863, 1908-1909, 1918-1919, and 1927-1928; in no case was there a third consec-utive year, but neither the preceding nor following years seem consistent.
Patterns frequently provide the foundation for a trading method or the justification forbeginning work in the development of a method. They have been applied in many ways toprice analysis, from the time of day to place an order to the compound relationship ofprice, volume, and open interest. Daily trading-opportunities may be a function of patternsbased on the strength or weakness of the daily opening price. These are discussed in thenext section. Weekly and weekend traits are studied, as well as types of reversals and theireffects. These techniques can be considered complementary when used sequentially, orthey can confirm the results of arother test when used together. The end of this chapterdiscusses more general issues in pattern recognition,
Pe recognition forms the basis for most trading systems. It is most obvious in tra-
‘The only other known work that concerns similar patterns, although for the stock market, is by Arthur A. Mer-rill, Bebavior of Prices on Wall Street (Analysis Press, Chappaqua, NY, 1966).PROJECTING DAILY HIGHS AND LOWS 383
 
 
FIGURE 15-| Graph of the New York Stock market.te
 
 
18-5
Sei
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
PROJECTING DAILY HIGHS AND LOWS
Statisticians claim that the best forecast of tomorrow’s price is today's price; they state thatno one has been able to reliably account for all the factors that would be needed to accu-rately project the changes that result in the high and low prices for tomorrow. Neverthe-less, many traders project these values and seem to use them with success.
Pivot Technique
The simplest approach to projecting tomorrow's highs and lows is to base those figures onthe average price of today plus or minus a value that somehow relies on the current trad-ing range, or volatility. One technique, based on a pivot point,” projects two levels of sup-port and resistance:
Pivot point P=(H+L+C)/2Resistance 1 RI=2xP-LSupport 1 _SL=2xP-HResistance 2 R2= (P-S1)+RlSupport 2 . S2=P-—(Ri1-SI)
DeMark’s Projected RangesAnother author and trader, Tom DeMark,° has based his projections on the positioning oftoday’s opening price relative to yesterday's closing price, which gives him added timely
? Mark Etzkorn, “All in a day's work,” Futures (January 95). This technique is attributed to William Greenspan.3 Tom DeMark, The New Science of Technical Analysis (Join Wiley & Sons, New York, 1994).384 PATTERN RECOGNITION
 
information. If today’s optn is higher than the previous close, the projections are biased
upward; if lower than the close, they are biased downward. |
1. If today’s close is below today's open, thenTomorrow's projected high = (H+C+2x1)/2-LTomorrow’s projected low = (H+ C+2x1)/2-H
2. If today’s close is above today’s open, thenTomorrow’s projected high = (2x H+1+C)/2-LTomorrow’s projected low = (2X H+L+C)/2-H
3. If today’s close is the same as today's open, thenTomorrow's projected high = (H+Z+2xC)/2-LTomorrow's projected low = (H+L+2xC)/2-H
Once the basic formula is determined, biasing tomorrow’s projection in the directionof today’s close relative to today’s open, then the projected high is found by removing twounits of the low price, and thie projected low is found by removing two units of the highprice from the formula. This effectively shifts the projection in the direction of the newhigh by one-half the difference of today’s close and today’s low, (C - )/2, and the new lowby one-half the difference of today’s close and today’s high, (H — C)/2.
Comparing the Two Ranges
Because the two methods, the pivot point technique and projected ranges, use the samebasic prices, combining them with simple multiples, it is not clear whether the results givevalues that are the same or different-For example, if the Deutschemark had a high, low,and close of 6600, 6450 and 6500, the first pivot method would give a projected first resis-tance level (high) of 2 x (6600 + 6450 + 6500)/3 — 6450 = 6583. DeMark’s projected high isdifferent based on how today’s opening price relates to the previous close. If the open islower than the previous close, we get (6600 + 6500 + 2 x 6450)/2 ~ 6450 = 6550; if theopen is higher, we have (2 x 6600 + 6450 + 6500)/2 — 6450 = 6625; and if the open is aboutthe same as the previous close, then the projected high is (6600 + 6450 + 2 x 6500)/2 —6450 = 6575. It seems reasonable that the pivot point method returns a value close toDeMark’s neutral case, when the market opens unchanged from the previous close.XN
TIME OF DAY
Market participants, especially floor traders, are the cause of periodic movement during theday. Angas called these the “tides of the daily prices.” Over the years, the great increase inparticipants has added liquidity to each pit but has not altered the intraday time patterns.
There are