RedK Compound Ratio Moving Average (CoRa_Wave)

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Compound Ratio Weighted Average (CoRa_Wave) is a moving average where the weights increase in a "logarithmically linear" way - from the furthest point in the data to the current point - the formula to calculate these weights work in a similar way to how "compound ratio" works - you start with an initial amount, then add a consistent "ratio of the cumulative prior sum" each period until you reach the end amount. The result is, the "step ratio" between the weights is consistent - This is not the case with linear-weights moving average (WMA), or EMA

- for example, if you consider a Weighted Moving Average (WMA) of length 5, the weights will be (from the furthest point towards the most current) 1, 2, 3, 4, 5 -- we can see that the ratio between these weights are inconsistent. in fact, the ratio between the 2 furthest points is 2:1, but the ratio between the most recent points is 5:4 -- the ratio is inconsistent, and in fact, more recent points are not getting the best weights they should/can get to counter-act the lag effect. Using the Compound ratio approach addresses that point.

a key advantage here is that we can significantly reduce the "tail weight" - which is "relatively" large in other MAs and would be main cause for lag - giving more weights to the most recent data points - and in a way that is consistent, reliable and easy to "code"

- the outcome is, a moving average line that suffers very little lag regardless of the length, and that can be relied on to track the price movements and swings closely.

other features:
- An accelerator, or multiplier, has been added to further increase the "aggressiveness" of the moving average line, giving even more weights to the more recent points - the multiplier will have more effect between 1 and 5, then will have a diminishing effect after that - note that a multiplier of 0 (which effectively causes a comp. ratio of 0 to be applied) will produce a Simple Moving Average line :)

- We also added the ability to use an "automatic smoothing" mechanism, that user can over-ride by manually choosing how much smoothing is used. This gives more flexibility to how we can leverage this Moving Average in our charting.

- User can also select the Resolution and Source price for the CoRa_Wave. by default, they will be set to "same as chart" and hlc3

here are the formulas for our Compound Ratio moving average:
Compound Weight ratio    r = (A/P)^1/t - 1
Weight at time t         A = P(1 + r)^t 
                           = Start_val * (1 + r) ^ index
index in the above formula is 0 for the furthest point out

Here's how CoRa_Wave compares to other common moving averages all set to the same length (20)

Proposed Usage
- CoRa_Wave can be used for any scenarios where we need a moving average that closely tracks the price, trend, swings with high responsiveness and little lag
- MA Cross-over scenarios - against another CoRa_Wave or any other MA
- below is a quick example scenario for how to utilize 2 CoRa_Wave lines of same length (one for open and one for closing price) to track swings and trends
- get as creative as you need :)

Code is commented - please feel free to leverage or customize further as you need.

👉 if you are interested in other moving averages i posted before, please check out the FiMA and the v_Wave ...
Quick update: CoRa_Wave is now dual color, more suitable for the visually oriented folks, like me!
- Restore chart

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