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Projection Bandwidth by Mel Widner
Projection Bands were developed by Mel Widner, Ph.D. They were originally
introduced in the July 1995 issue of Technical Analysisof Stocks and Commodities magazine.

Projection Bands are similar in concept to other types of bands including moving average bands, Price Channels (see Price Channel), Envelopes (seeEnvelope), and BollingerBands (see Bollinger Bands). They also have some of the characteristics of channel lines such as RaffRegressionChannels (see Raff Regression Channel).

Projection Bands are plotted by finding the minimum and maximum prices over the specified number of days
and projecting these forward (parallel to a linear regression line). The resulting plot consists of two bands representing the minimum and maximum price boundaries.Prices will always be contained by the bands, unlike Bollinger Bands.


Projections Bands are used much like other types of bands--they help gauge the ebb and flow of optimism and pessimism. When prices are at or near the upper band, extreme optimism is indicated--lookfor prices to move down to more rational levels. Likewise, when prices are at or near the lower band, extreme pessimism isindicated--look for prices to move up to more rational levels.

It is recommended that all band generated signals be confirmed by other indicators, because prices will often ride along a band for an extended amount of time during strong trending markets.

During trending markets, you can use bands to trade short-term reactionsagainst the primary trend. In trading range markets, you can use the bands to trade overbought/oversoldlevels. Indicators like the VHF (see Vertical Horizontal Filter), CMO (see ChandeMomentum Oscillator), and r-squared (see r-squared) can be used to gauge the trendiness of themarket.)

Slope of High

{14 period regression line of High)}
((14 * (Sum( Cum(1) * HIGH, 14))) - (Sum( Cum(1),14) * ( Sum(HIGH, 14)))) /
((14 * Sum( Pwr( Cum(1), 2), 14)) - Pwr( Sum(Cum(1),14), 2))


Slope of Low

{14 period regression line of Low}
((14 * (Sum( Cum(1) * LOW, 14))) - (Sum( Cum(1), 14) * ( Sum(LOW, 14))))/
((14 * Sum( Pwr( Cum(1), 2), 14)) - Pwr( Sum(Cum(1),14), 2))



Upper Projection Band

Max( Ref(HIGH,-1) + 1 * Fml("slope of high"),
Max( Ref(HIGH,-2) + 2 * Fml("slope of high"),
Max( Ref(HIGH,-3) + 3 * Fml("slope of high"),
Max( Ref(HIGH,-4) + 4 * Fml("slope of high"),
Max( Ref(HIGH,-5) + 5 * Fml("slope of high"),
Max( Ref(HIGH,-6) + 6 * Fml("slope of high"),
Max( Ref(HIGH,-7) + 7 * Fml("slope of high"),
Max( Ref(HIGH,-8) + 8 * Fml("slope of high"),
Max( Ref(HIGH,-9) + 9 * Fml("slope of high"),
Max( Ref(HIGH,-10) + 10 * Fml("slope of high"),
Max( Ref(HIGH,-11) + 11 * Fml("slope of high"),
Max( Ref(HIGH,-12) + 12 * Fml("slope of high"),
     Ref(HIGH,-13) + 13 * Fml("slope of high"))))))))))))))



Lower Projection Band

Min( Ref(LOW,-1) + 1 * Fml("slope of low"),
Min( Ref(LOW,-2) + 2 * Fml("slope of low"),
Min( Ref(LOW,-3) + 3 * Fml("slope of low"),
Min( Ref(LOW,-4) + 4 * Fml("slope of low"),
Min( Ref(LOW,-5) + 5 * Fml("slope of low"),
Min( Ref(LOW,-6) + 6 * Fml("slope of low"),
Min( Ref(LOW,-7) + 7 * Fml("slope of low"),
Min( Ref(LOW,-8) + 8 * Fml("slope of low"),
Min( Ref(LOW,-9) + 9 * Fml("slope of low"),
Min( Ref(LOW,-10) + 10 * Fml("slope of low"),
Min( Ref(LOW,-11) + 11 * Fml("slope of low"),
Min( Ref(LOW,-12) + 12 * Fml("slope of low"),
     Ref(LOW,-13) + 13 * Fml("slope of low"))))))))))))))



Projection Bandwidth

200 *
(Fml("Upper Projection Band") - Fml("Lower Projection Band")) /
(Fml("Upper Projection Band") + Fml("Lower Projection Band"))



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