NoNoiseMA & Slope

Happy trade,

This is a noise-reduced moving average — let's call it the No-Noise MA. A MA where false breakout price action should have little to no impact, while the main trend remains fully represented. In comparison to previous MAs this one's trend appear more linear, and sideways price actions becomes easier to detect thanks to it's unique two filter stages.

In short, the No-Noise-MA (Noise-Reduced Moving Average) is calculated as the cumulative sum of the slopes derived from the center line of the last x pivot points. Let’s break it down step by step:

Pivot Detection:

A pivot algorithm (an adapted variant of the Bilson-Gann-Count method) identifies consecutive pivot points (high, low, high, low, etc.) in the close price series. Let's call this set of Pivots S.

Center Line Calculation:

Out of the set S the last x pivots are used to compute a center line (linear regression line). Always when a new pivot is confirmed, the oldest pivot in the queue is removed, and the new pivot is added.

Slope Extraction:

The center line is defined by its equation shown in the image below
Image 1


Cumulative Slope Sum:

As shown in the image 1 the slope is a series with values around zero. The No-Noise-MA is then just the cumulative sum of the slope series and a correction term. A correction term is needed otherwise the No-Noise-MA would run away over time from the original close price. The correction term is just the deviation between close price and cumulative slope sum multiply with a factor around 0.01 added to the No-Noise-MA.

Noise Reduction:

The goal of noise reduction is done by two filter stages. First Filter is the reduction of the input values. As shown above not all bars close prices are use, instead it uses just the pivot points delivered by the Bilson-Gann-Count method. Favorable the Bilson-Gann-Count method delivers the Pivot points in most cases much faster as other Pivot methods. Already after two bars a new Pivot is confirmed. This takes out all ups and downs between two consecutive Pivots. This first filter stage is legit because all price action in between is hedged by the Pivots.

The second filter stage is the done by the length of the center line. As more pivots are used to calculate the center line as smoother the slope becomes. Out liners just gets less impact if the base is bigger. So the number of involved Pivots has the same meaning as the lengths in any other MA.

Comparison with usual MAs:

For a comparison with other MAs this script also calculate the average lengths of the center line, shown in the upper right chart. So choose for example SMA and set the length parameter to the average length of the center line. As shown in the following image 2.
Image 2

This way both MAs have the same data base and can be objectively compared.

Trend detection:

The slope of the center line can be used for trend confirmation. A slope bigger then zero is an up trend while a slope smaller then zero is a down trend. And side way price action is indicated when the slope is around zero within a certain threshold.
Image 3

One hint should be mentioned here. The side way section gets indicated much later. About the number of bars as the center line is long. Before that there are just up or down trend predicted. In the image 2 you see the slope is firstly tin and as more bars past by the slope becomes more thick. This should indicate the point where no side way predictions will happens anymore.

Variation of calculation

In the settings menu you can find the setting "Include last close to center line". With this activated the center line is calculated with the last pivots and the last close price. The last close price is assumed as a pivot too. This gives the slope a more early reaction to volatile price action. But also brings back some noise.