15433 + - iyi

Greatest magnitude of solar eclipse = -q 545 . 2u- Lunar Eclipses

For a lunar eclipse, y \c2&t distance for the center of the moon 10 the Earths shadow (see Figure 14-25). The value yis positive if the moons center is passing north of the axis of the shadow and negative if it is passing south. At the distance of the moon, the pienum-bra radius p = 1.2847 + and the umbra radius a=0.7404 - u. The magnitude of the lunar eclipse is

penumbralecHpses. (1.5572 + - )/0.5450

umbral eclipses: (1.0129 - - ) / 0.5450

If the magnitude is less than zero, there is no eclipse. The semidurations of the partial and total phases in the umbra are calculated as

/•=1.0129-

T= 0.4679 -

= 0.5458 + 0.0400 cos M

and the semidurations in minutes are

panial phase = - vp - y

total phase = vt" - y

Example! Solar eclipse of May 21,1993:

The foUcwang values can be used to verify your calculations:

May 21 is the 141st day of the year, therefore k = 1993 + 14 65 = 1993.38 T= 1993.38/1236.85 = I.6ii6. JDE = 2449128.5894

FIGURE 14-25 Geometrj of a lunar eclipse.

= 135.9142 = 1842

= 244*.5757 6 = 5-3589

F=1657296 = 1.1348

= 253 .0026 = 0.0097

Ft = 165.7551

Because 180" - F is between 13 9 and 12.0 the eclipse is uncertain, and because is between a9972 and 1 5433 + u 1 553, the eclipse is partial. By calculating the greatest magnitude of a solar eclipse we get 0.740. Because F is near 180°, the eclipse occurs near the moons descending node, and because is positive, the eclipse is visible in the northern hemisphere of the Earth. By addirig the corrections to JDE, the final time of maximum eclipse IS 2449129-0979, which corresponds lo May 21, 1993. at 14h21m0s TD. This differs from the exact value of I4h20ml4s TD by less than 1 minute.

15 Pattern Recognition

Pattem recognition forms the basis for most trading sjstems. It is most obvious m traditional charting, which is entirely the identification of common formations even mo\ing averages attempt to isolate, using mathematical methods, what has been \isually determined to be a trend. Traders have alwajs looked for pattems in price movement Because they were not equipped with computers, their conclusions are considered market lore rather than feet and are handed down fi-om generation to generation as proverbs, such as "Up on Monday, down on Tuesday "Locals even up on Fridajs and "Watch for key reversals." Because these three sajings have endured, they are candidates for analjsis later in this chapter.

The earliest technical sjstems based on pattems were of the form:-Ifefier a sharp rise the maiket faus to advance for 3 dajs, then sell.-As computers became more powerfiil. more complex approaches could be taken. For example, by obser\ing the closing prices starting on an arlatrarj day, all pattems of higher and lower closes can be recorded to find their tendencj to repeat. A computer is well-equipped to perform this task. First, the 2- and 3-day pattems are eliminated because the recurrence of up-down or down-up and the equi\alent 3-day pattems would be too fi-equent to be meaningful Then, the closing prices are scanned for occurrences of predefined pattems. For example, if an up-up-down-up down-up is to be matched, every six consecutive prices must be tested. From a table of occurrences we can conclude that these pattems can be predicted in ad\ance or that they are leading indicators of other price moves. This approach, as well as the comlanation of events used to forecast profitable situations, are discussed later in this chapter.

Pattem recognition may appear to be more of a game than a business, but it is a source of many \aluable ideas. Figure 15-1. a graph of the New York Stock Exchange (1854-1959). shows the simplification of pattems to the point where it is difEcult not to coimt the recurrences of the more obvious pattems and look for the formations that precede them to see whether they could be predictive. For example, in 1922, 1924, and 1927 there were sharp advances in the market. the years preceding those showed an identical U pattem. It would be interesting to see whether another occurrence of a sjmnietric U was followed by a similar rise. Another pattem that stands out is that of two consecutive years of shmp rise. 1862-1863, 1908-1909, 1918-1919, and 192*-1928; in no case was there a third consecutive year, but neither the preceding nor following years seem consistent.

Pattems fi-equently provide the foimdation for a trading method or the justification for binning work in the development of a method They have been applied in many- wajs to price analjsis, fi-om the time of day to place an order to the compoimd relationship of price, volimie, and open interest. trading opportunities may be a function of pattems based on the stiength or weakness of the dauy opening price These are discussed in the next section. Weekly and weekend traits are studied, as well as tjpes of reversals and their effects. These techniques can be considered complementarj when used sequentially, or they can confimi the results of another test when used together The end of this chapter discusses more general issues in pattem recognition.

The only other known work that concems similar pattems, although for the stock market, is by Arthur A Merrill, Bebavior of prices on Wall Stieet (Analjsis Press. CTiappaqua. NY 1966).

FIGURE 15- 1 Graph oftiieNewYork Stock market.