here we take a step further - instead of using equal weight for the moving average (as in the Simple moving average) or linear weights (as in the weighted moving average), we get to pick THE MAGIC SEQUENCE, Fibonacci.
we will use the Fibonacci Sequence as weights to produce our moving average - so practically, we create a "Fibonacci Weighted Moving Average" (let's call it FiMA) - and compare the result with other commonly-used moving averages of the same length
in a Fibonacci moving average, the data will be weighted based on the Fibonacci Series starting from 1 (for the furthest data point)
so for example, if we use a length of 10, the weights will be 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 with the 55 being the weight applied to the most recent / current bar's selected value (close, hl2, hc3..etc) and moving backward
before i posted this script, i searched around to see if someone else has already wrote this - i found a couple, but the approach we use here in this code is different - i can't claim it to be more efficient - i honestly don't know - but the resulting code here, IMHO, is more compact and easier to integrate in other studies that you may like to put together to leverage this idea, to create your own indicators and strategies.
the reason the code here is more compact, is that it utilizes a shorter formula to calculate the FIb(n) - i included the source where i found that formula, and i tested it before using it in the code.
i also added an optional "extra smoothing" for the resulting MA, by simply calling the fima() function a second time (so like doing a 2-pass filter), with a smaller length on the result of the 1st pass. keep this smoothing small not to produce too much lag.
i like the outcome when compared to other moving averages - it has a fast response to data/trend change and less overshoot - but honesty i didn't see any real "Fibonacci Magic" :) .. but i'll leave the final judgement to those who use it - this is more of an experimental code in all cases - please feel free to use, change and share feedback.
1. we removed the round() function from the calculation of the Fib Weights. it only makes a small difference until Fib(9) but it causes a side effect of the FiMA behaving erratically after length = 92 (this is where the function hits the maximum integer value in Pine)
2. thanks to feedback - yes, as the FiMA length increases, the Fib ratios become too large .. at around length = 15 to 20, the last 5 data points will always have ~91% of the sum of weights - any length changes after that will have no effect on the FiMA line plot. if this MA is used, it's suggested that it is used only for short lengths below 15 - otherwise, a weighted moving average will be a lot more efficient.
at the end, this was an experimental TA exercise - maybe someone gets inspired and makes something out of it :)
- thanks to those who provided feedback and helped diagnose the behavior with high value of lengths
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