Editing Moving average (section)

==Other weightings==
Other weighting systems are used occasionally – for example, in share trading a '''volume weighting''' will weight each time period in proportion to its trading volume.

A further weighting, used by actuaries, is Spencer's 15-Point Moving Average<ref>[http://mathworld.wolfram.com/Spencers15-PointMovingAverage.html Spencer's 15-Point Moving Average — from Wolfram MathWorld<!-- Bot generated title -->]</ref> (a central moving average). Its symmetric weight coefficients are [−3, −6, −5, 3, 21, 46, 67, 74, 67, 46, 21, 3, −5, −6, −3], which factors as {{sfrac|[1, 1, 1, 1]×[1, 1, 1, 1]×[1, 1, 1, 1, 1]×[−3, 3, 4, 3, −3]|320}} and leaves samples of any quadratic or cubic polynomial unchanged.<ref>Rob J Hyndman. "[https://robjhyndman.com/papers/movingaverage.pdf Moving averages]". 2009-11-08. Accessed 2020-08-20.</ref><ref>Aditya Guntuboyina. "[https://www.stat.berkeley.edu/~aditya/Site/Statistics_153;_Spring_2012_files/Spring2012Statistics153LectureThree.pdf Statistics 153 (Time Series) : Lecture Three]". 2012-01-24. Accessed 2024-01-07.</ref>

Outside the world of finance, weighted running means have many forms and applications. Each weighting function or "kernel" has its own characteristics. In engineering and science the frequency and phase response of the filter is often of primary importance in understanding the desired and undesired distortions that a particular filter will apply to the data.

A mean does not just "smooth" the data. A mean is a form of low-pass filter. The effects of the particular filter used should be understood in order to make an appropriate choice. On this point, the French version of this article discusses the spectral effects of 3 kinds of means (cumulative, exponential, Gaussian).