Calculation of RgressionChannels

[lakman184]

Hi,

I have a question.

I use a regression channel with 304 periods and a width of 4. That means I have a standard deviation of 2 by each side (95,45%).

With 304 periods I would expect to see ~13 bars outside the channels (304 - (304 * 0.9545) = 13.83). But I only observe 1 single bar outside.


Thank you,
Lukas

[NinjaTrader_Jim]

Hello Lukas,

Thanks for your post.

Width represents the number of standard deviations the upper and lower channels are drawn from the middle regression line.

Below is the relevant code which shows how the line is drawn from the calculated standard deviation, multiplied by width.

int [B]stdDevPixels [/B]= (int) Math.Round((([B]stdDev[/B]*[B]Width[/B])/(chartScale.MaxValue - chartScale.MinValue))*panel.H, 0);

...
// Middle
RenderTarget.DrawLine(startVector, endVector, Plots[0].BrushDX, Plots[0].Width, Plots[0].StrokeStyle);

// Upper
RenderTarget.DrawLine(new Vector2(startVector.X, startVector.Y - [B]stdDevPixels[/B]), new Vector2(endVector.X, endVector.Y - [B]stdDevPixels[/B]), Plots[1].BrushDX, Plots[1].Width, Plots[1].StrokeStyle);

// Lower
RenderTarget.DrawLine(new Vector2(startVector.X, startVector.Y + [B]stdDevPixels[/B]), new Vector2(endVector.X, endVector.Y + [B]stdDevPixels[/B]), Plots[2].BrushDX, Plots[2].Width, Plots[2].StrokeStyle);

The standard deviation is calculated in OnBarUpdate:

double stdDeviation = Math.Sqrt(sumResiduals / Math.Min(CurrentBar + 1, Period));
stdDeviationSeries[0] = stdDeviation;

You may check the source code for the Regression Channel indicator for a further look into how it's calculations are made. Below is a link to our Help Guide documentation which also contains an brief explanation of the indicator.

https://ninjatrader.com/support/helpGuides/nt8/regression_channel.htm

We look forward to assisting.

[lakman184]

Hi Jim,

thanks for your quick reply and the explanation. But I still don't understand the calculation.

The chart attached shows a regression over 100 bars and a std.dev (Width) of 2.

Considering your explanation above, I would assume to observe 4.55 Bars with close price outside the upper deviation line. 2 std. dev = 95,45%. 100 bars - 95.45 bars = 4.55 bars.

But I don't observe 4 or 5 bars outside but 8, that is twice as many.

[NinjaTrader_Jim]

Hello lakman184,

I apologize for a delayed response as I wanted to test this further and I had some questions myself.

Width determines the standard deviation in one direction, so Width would be need to be doubled and set to 4 to simulate a regular standard deviation of 2.

The distribution also is not technically a normal distribution. A Residual Distribution is used instead.

A publicly available resource can be found here - https://www.investopedia.com/terms/r...-deviation.asp

We look forward to assisting.