In statistics, the moving average is usually defined for discrete data sets. Is there a moving average concept for continuous randomly fast-oscillating functions? I am seeking for the moving average determined in terms of integrals rather than sums.


1 Answer 1


You could simply use the mean value of the function in each window.

A "backward-looking" moving average with window size $w$ is $$ \mbox{MA}_w^\text{b}(t) = \frac{1}{w} \int_{t-w}^t f(x)dx , $$ and a "centered" moving average is $$ \mbox{MA}_w^\text{c}(t) = \frac{1}{w} \int_{t-w/2}^{t+w/2} f(x)dx . $$

  • $\begingroup$ Seems nice! Do you have a reference to a textbook or paper where this definition is utilized? $\endgroup$
    – freude
    Apr 27, 2014 at 19:38
  • $\begingroup$ I don't have a reference where the suggested function is used to compute the moving average; I just customized the first mean value theorem to your needs. $\endgroup$
    – QuantIbex
    Apr 28, 2014 at 5:49

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