Endnotes

three side-by-side charts featuring increasing time frames from left to right.

Chapter 9

1. There are two calculations for standard deviation, sample and population. The difference is the final divisor, which is n - 1 for the sample and n for the population.

2. GARCH (generalized autoregressive conditional heteroskedas-ticity) and ARCH (autoregressive conditional heteroskedasti-city) are mathematical theories that focus on cyclicity in volatility. For more information see the MathWorks tutorial chapter on GARCH at http: www.mathworks.com/access/ helpdesk/help /toolbox/ garch/chap 1 tu.shtml. While the whole chapter may be a bit much for most, the first part offers a nice, if terse, overview.

Chapter 10

1. A full discussion of technical patterns is beyond the scope of this book. See Schabacker or Edwards and Magee in the Bibliography.

2. The Lennox System by Sam Kash Kachigan, author of Statistical Analysis (see the Bibliography).

3. A fractal displays the same patterns at all levels of magnification. So if a head-and-shoulders pattern were found at the top of the right shoulder of a larger head-and-shoulders pattern the patterns could be said to be fractal. Fractals occur frequently in chaotic systems. A good read on this subject is Chaos by James Gleick, New York: Viking, 1987.

Chapter 11

1. For futures contracts, point filters may offer a better view due to the way margin works. When entering into a futures contract, you do not put up the full value of the contract; rather you put up a good-faith deposit, margin, that is the same without regard to price level. So a 1-point move at 20 has the same economic value to a trader as a 1-point move at 100.

2. Macauleys work on the square root rule was most likely done in the early 1930s. But I have been unable to track down the

Endnotes

appropriate issues of the Annalist to confirm this. This is the same Fred Macauley who brought you Macauleys modified duration, the standard volatility measurement for bonds. For more on the SRR, see Norm Fosback in Stock Market Logic (see the Bibliography).

3. Bollinger Boxes are directly supported by RTRs TechniFilter Plus. To view Bollinger Boxes in TechniFilter, use the form nnmm% for the box size, where nn is the multiplier and mm is the power in the formula O.nn * lastA0.mm. For simplified Bollinger Boxes, enter 1750 percent for "Boxsize," 3 for "Reversal," and High:Low for "Use" (evaluation method). Our thanks to Clay Burch for his help in this regard (http: www.rtrsoftware.com).

4. The failure of his test is probably due to his use of each stocks volatility as the filter mechanism, which filtered out much of the signal in addition to the noise. When the institutional trading platform www.PatternPower.com was built using the same patterns but Bollinger Boxes instead of a volatility filter, significant results were achieved.

5. Both a capital M and a capital W consist of four strokes connecting five points. There are 32 possible patterns using five points, 2A5.

Chapter 12

1. Mark Douglas defines greed as "fear of not having enough" in his thought-provoking book The Disciplined Trader (see the Bibliography). It is interesting to ponder the manifestations of these emotions in that crucible that we call the marketplace; in other words, a market analysts job is an interesting one by definition.

2. "Down is faster" can be empirically demonstrated. One example: In the spring of 2000 a lightning bear market struck the NASDAQ and the composite fell 37 percent, erasing in 3 weeks gains that had taken 4% months.

Chapter 13

1. To my mind it is easiest to stick with a series of Ms when analyzing a head-and-shoulders formation, as they are

Endnotes

logically consistent with tops, just as Ws are logically consistent with bottoms.

Chapter 14

1. Indicators such as volume indicators generally come in one of two forms, open or closed. Open-form indicators are usually calculated by keeping a running sum from the point of inception-usually the first data point. Closed-form indicators may also be a sum, but of a given number of periods, 10 or 20 for example. Open-form indicators are usually plotted in the same clip as price to allow direct comparisons, while closed-form indicators are usually plotted in their own clips and are often referred to as oscillators.

2. Elliotts wave pattern can be shown to be a combination of three underlying cycles, where each cycle after the first (shortest) is double the length of the prior cycle. (Once again, the three disparate time frames appear!) This process was demonstrated in my 1986 paper on the subject. Accompanying that paper was a short computer program written in Microsoft BASIC that allowed you to experiment with combining cycles of any lengths and examine the resulting patterns.

Chapter 15

1. The mathematically inclined will quickly note that BandWidth equals four times the standard deviation divided by the mean. The statistically inclined will note that this is four times the coefficient of variation.

2. A more complicated definition of The Squeeze that is taught at our seminars involves Bollinger Bands on volatility itself. First plot the 20-day standard deviation of the close, or typical price. Now plot the 125-day, 1.5 standard deviation width Bollinger Bands of the standard deviation just plotted. A Squeeze is triggered when the 20-day standard deviation tags the lower band.

3. Perhaps the head fake is a corollary of the old "sell on the news" idea. As the new information flows into the market, might traders be taking advantage of it to shift positions,