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Throughout this book, we ll be learning about a variety of patterns, a number of which are known as reversal patterns. They are called this because they forecast a reversal in price direction. One of the most basic and powerful reversal patterns is called the head and shoulders. These formations are pretty easy to spot: on the left side is a hump in prices (gradually moving up and then moving down again to a certain supporting price). In the middle is a taller hump, again, slowly moving up and then down again to support. This is the head. Finally, there is another hump, the smallest of the three (ideally), which is the right shoulder. The support line is what s key here. It even has a special name in the context of this pattern; instead of being called the support line, it s called the neckline. If prices break beneath the neckline, there are three general possibilities:

!(dx)m(x)H*(x) = ~ Lm(k)H*(k) V ! (dx)lm(x)1 = ~ Lm*(k)m(k) 1 (dx)lm(x) I = V3 L 8 (k 1 + k !

(17.10) k3 k4 )

Note: See the Resize and Move Objects section, earlier in this chapter, to learn how to resize an image.

m*( k1)m*( k 2 )m (k 3 )m (k 4 )

If m (x) is real, each k sum above should extend only over a hemisphere instead of the entire k space, (or one could take half the sum over the entire k space.)

Functional Integration A practical way to do the functional integral in (17.1) is to replace the continuous d-dimensional space by a discrete lattice of spacing a, which is of the order of atomic distances. We then regard the value of m(x) at each lattice site x to be an independent number, and integrate them separately:

!(Dm)

dm (x)

(17.11)

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1. The prices will sink from there. 2. Prices will sink brie y, recover to touch the underside of what used to

where the product is taken over all the lattice sites x. The lattice constant also serves as a cutoff. Another way to define the functional integral is to integrate each Fourier component m(k) separately and independently, for Ikl < A:

!(Dm)

! dm(k) dm*(k)

1 2 3 4

(17.12)

The integral! dm(k) dm*(k) is a two-dimensional integration over the complex plane of m(k), equivalent to integrating the real and imaginary parts independently. The limit L ~ 00 here is independent of the more difficult limit A ~ 00.

The product in (17.12) extends over all of k space (subject to the cutoff condition) if m(x) is complex, but only over a hemisphere if m(x) is real. In the latter case, it might be simpler to allow k the full space, and to take the square root of the answer later.

The only functional integral we can do exactly is of the Gaussian type:

1= f(Dep)exp f(dx)[ -~IV'ep(x)12 - ~roep2(x) + ep(x)1](x)]

be support (now resistance), and then start to fall. 3. Prices will stabilize, push back toward the former support line, and then overcome it, thus negating the pattern. The ideal circumstance is (2), since it allows a person to carefully enter the position at a very desirable price and set a stop just above the

j(Dep) exp [- Hep, K, ep) + (1], ep)]

(17.13)

where the last form rewrites the x integral as an inner product, with K == ro - V' 2. One can obviously do the integral by Fourier analyzing ep and using (17.12). There is, however, a shortcut. Consider the elementary integral (done by completing the square) oo dep 1 _ _ e-(1/2)K</>2+~</> = _ e~2 12K (17.14)

f(Dep)exp[-Hep,Kep) + (1],ep)}

Click the object you want to crop. Click the Format tab. Click the Crop Click Crop to Shape and choose the desired shape from the menu.

(detK)-1/2 exp H1],K- 11]) (17.15)

has the meaning given in (17.11) or (17.12). This formula is invariant under a unitary transformation of the vector ep, which generally transforms K into a nondiagonal matrix. Following are some examples of the inner product: Discrete:

x space:

k space:

up and down, this parallel line will follow your mouse movement. 5. Place the line at its destination and click the mouse button to complete the drawing. You will now have a drawn channel. As with the trendline, you can right-click on a drawn channel (Figure 8.7) to make use of other features, one of which is unique to the channel. Here is what each item from the menu does:

(A, B)

(17.16)

(A,B) = j(dx)A(x)B(x)

(A, B)

k V---'

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