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$$ \text{WMA}_n = w \ p_n + (1-w) \text{WMA}_{n-1} $$

This function, given weight $0 < w ≪ 1 $, creates a neat smoothing of "noisy" input data $p$, a kind of weighted moving average. Due to numerical simplicity, and minimal memory requirements, I've been using it frequently for realtime smoothing of noisy input data. But whenever I'm asked "what function is that?" I draw a blank, "some kind of weighted moving average." Obviously this doesn't quite sell the algorithm when I propose it.

This approach is so simple and efficient I'm completely sure it's been invented and used before - and surely, named. If so - what is this moving average function called?

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This is an AR|ARX model - Auto-Reggresive | with eXogenous input:

https://en.m.wikipedia.org/wiki/Autoregressive–moving-average_model https://www.mathworks.com/help/ident/ug/identifying-nonlinear-arx-models.html

I am so sorry, somebody already invented them. Some guys called Box & Jenkins (though prior references were used before). A lot of people use them everyday.

In fact there is a whole Stack Exchange community for them!! https://dsp.stackexchange.com/

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