G-Channels - Efficient Calculation Of Upper/Lower Extremities

Introduction

Channels indicators are widely used in technical analysis, they provide lot of information. In general, technical indicators giving upper/lower extremities are calculated by adding/subtracting a volatility component to a central tendency estimator. This is the case with Bollinger bands, using the rolling standard deviation as volatility estimator and the simple moving average as central tendency estimator, or the Keltner channels using the exponential moving average and the average true range.

Lots and lots and lots (i can go on) of those indicators have been made, they only really need a central tendency estimator, which can be obtained from pretty much any filter, however i find interesting to focus on the efficiency of those indicators, therefore i propose a super efficient channel indicator using recursion. The average resulting from the upper/lower extremity of the indicator provide a new efficient filter similar to the average highest/lowest.

The calculation - How Does It Works

Efficiency is often associated to recursion, this would allow us to use past output values as input, so how does the indicator is calculated? Lets look at the upper band calculation :

a := max(src,nz(a(1))) - nz(a(1) - b(1))/length

src is the closing price, a is upper extremity, b is the lower one. Here we only need 3 values, the previous values of a and b and the closing price. Basically a := max(src,nz(a(1))) mean :

if the closing price is greater than the precedent value of a then output the closing price, else output the precedent value of a

therefore a will never be inferior to its precedent value, this is useful for getting the maximum price value in our dataset however its not useful to make an upper band, therefore we subtract this to a correction factor defined as the difference between a and b, this force the upper band to have lower values thus acting like a band without loosing its "upper" property, a similar process is done with the lower band.

Of course we could only use 2 values for making the indicator, thus ending with :

a := max(src,nz(a(1))) - nz(abs(close - a(1))/length

In fact this implementation is the same as the one proposed in my paper "Recursive Bands - A New Indicator For Technical Analysis", its also what i used for making the indicator "Adaptive Trailing Stop", this would be more efficient but i used the difference between the upper and lower extremities for a reason.


The Central tendency Estimator

This is the reason why i didn't implemented a more efficient version. Basically this central tendency estimator is just the average between the upper and lower extremities, it behave like the average of the highest/lowest over length period, its central plot in the Donchian channel indicator. Below is a comparison of both with length = 100 :


But why is our average so "boxy"? The extremities are not boxy, so why the average is sometimes equal to its previous value? Explain!

Its super easy to understand, imagine two lines, if their absolute change is the same and they follow an opposite direction, then their average is constant.


the average of the green and red line is the orange line. If both lines follow the same direction then their average will also follow this direction.


When both extremities follow the same direction, the average will also do the same, when both follow an opposite direction then the average will be equal to its precedent value, this is also due to the fact that both extremities are based on the same correction factor (a-b), else the average wouldn't act that way, now you understand why i made this choice.

Conclusion

I proposed an efficient implementation of a channel indicator that provide an interesting central tendency estimator. This simple implementation would allow for tons of interesting concepts, some of my indicators use a similar approach and allow for great outputs, you'll see them soon enough. I hope this indicator find its use in the community, remember to ask before using this indicator in a script you want to publish.

Thanks for reading !

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