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Standard Error Bands by Jon Anderson
rev. 01/06/97 For interpretation refer to the article "Standard Error Bands", in the September 96
issue of TASC, written by Jon Anderson. Here are the MetaStock formulas for calculating the indicators used in my article, "Standard error bands"

21 Period Upper Band (smoothed)

Mov((21 * Sum(Cum(1) * C,21) - Sum(Cum(1),21) * Sum(C,21)) /
(21 * Sum(Pwr(Cum(1),2),21) - Pwr(Sum(Cum(1),21),2))* Cum(1) +
(Mov(C,21,S) - Mov(Cum(1),21,S) * (21 * Sum(Cum(1)* C,21) -
Sum(Cum(1),21) * Sum(C,21))/ (21 * Sum(Pwr(Cum(1),2),21)-
Pwr(Sum(Cum(1),21),2))) +2*(Sqrt(((Sum(Power(C,2),21)-
Power(Sum(C,21),2)/21))- ((Sum(Cum(1)*C,21))-((Sum(Cum(1),21)*Sum(C,21)/21)))/
((Sum(Power(Cum(1),2),21)) - (Power(Sum(Cum(1),21),2)/21)) *
((Sum(Cum(1)*C,21))-((Sum(Cum(1),21)*Sum(C,21)/21))))/19),3,S)

21 Period Lower Band (smoothed)

Mov((21 * Sum(Cum(1) * C,21) - Sum(Cum(1),21) * Sum(C,21)) /
(21 * Sum(Pwr(Cum(1),2),21) - Pwr(Sum(Cum(1),21),2))* Cum(1) +
(Mov(C,21,S) - Mov(Cum(1),21,S) * (21 * Sum(Cum(1)* C,21) - Sum(Cum(1),21) *
Sum(C,21))/ (21 * Sum(Pwr(Cum(1),2),21) -Pwr(Sum(Cum(1),21),2))) -
2*(Sqrt(((Sum(Power(C,2),21)-(Power(Sum(C,21),2)/21))-((Sum(Cum(1)*C,21))-
((Sum(Cum(1),21) * Sum(C,21)/21))) / ((Sum(Power(Cum(1),2),21))-
(Power(Sum(Cum(1),21),2)/21))*((Sum(Cum(1)*C,21))-
((Sum(Cum(1),21)*Sum(C,21)/21)))) /19)),3,S)

21 Period R2 (smoothed)

Mov((Pwr(Corr(Cum(1),C,21,0),2)),3,S)

21 Period Regression Slope

(((Sum(Cum(1)*C,21))-(Sum(Cum(1),21)*Sum(C,21)/21)) /
((Sum(Power(Cum(1),2),21))-(Power(Sum(Cum(1),21),2)/21)))

21 Period %A

((C-Fml("21 Period Lower Band (smoothed)"))/
(Fml("21 Period Upper Band (smoothed)") -
Fml("21 Period Lower Band (smoothed)")))

21 Period Regression (smoothed)

Mov((21*Sum(Cum(1)*C,21)-Sum(Cum(1),21)*Sum(C,21)) /
(21*Sum(Pwr(Cum(1),2),21) - Pwr(Sum(Cum(1),21),2))*Cum(1) +
(Mov(C,21,S)- Mov(Cum(1),21,S)*(21*Sum(Cum(1)* C,21) -
Sum(Cum(1),21)*Sum(C,21))/(21*Sum(Pwr(Cum(1),2),21)- Pwr(Sum(Cum(1),21),2))),3,S)

Binary Bandwidth Indicator

If((ATR(55)/(BBandTop(C,21,S,2) - BBandBot(C,21,S,2)))>.50,+1,0)

Jon Andersen, Equis International

Standard Error Bands are a type of envelope (see Envelope) developed by Jon Andersen.
They are similar to Bollinger Bands in appearance, but they are calculated and interpreted quite differently.
Where Bollinger Bands are plotted at standard deviation levels above andbelow a moving average, Standard Error Bands are plotted at standard error levels above and belowa linear regression plot. See Standard Error for a definition of standard error.

For more information on other channel-based line studies, see Envelope, Price Channel, Raff Regression Channel, Standard Deviation Channel , and StandardError Channel .

When displaying Standard Error Bands, you are prompted to enter the number of periods in the bands and the number of standard errors between the bands and the linear regressionline (see Standard Error Bands).
Mr. Andersen recommends default values of "21" for the number of periods, a 3-day simple moving average for the smoothing, and "2" standard errors. He also notes that veryshort time frames tend to produce unreliable results.

MetaStock plots Standard Error Bands on the security's prices or indicator.
These interpretational comments refer to bands on the security's closingprice.

Because the spacing between Standard Error Bands is based on the standard error of the security, the bands widen when the volatility around the current trend increases, andcontract when volatility around the current trend decreases.

Since Standard Error Bands are statistically based, other statistical indicators such as r-squared, Standard Error, Linear Regression, etc. work well fortrade confirmation. Mr. Andersen notes the following characteristics of Standard Error Bands.

· Tight bands are an indication of a strong trend.
· Prices tend to bounce between the bands when the bands are wide.
· Tight bands followed by a widening of the bands mayindicate the exhaustion of a trend and a possible reversal.
· When the bands reverse direction after an exhausted trend,prices tend to move in the direction of the bands.
· The r-squared indicator works well in combination with Standard Error Bands.

A high r-squared value combined with tight bands confirms a strong trend.
A low r-squared value combined with wide bands confirms that prices are consolidating.

Source / From: TOP
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