Editing Moving average (section)

{{Short description|Type of statistical measure over subsets of a dataset}}
{{Other uses|Moving-average model|Moving average (disambiguation)}}
[[File:Lissage sinus bruite moyenne glissante.svg|thumb|Smoothing of a noisy sine (blue curve) with a moving average (red curve).]]

In [[statistics]], a '''moving average''' ('''rolling average''' or '''running average''' or '''moving mean'''<ref>[http://www.waterboards.ca.gov/waterrights/water_issues/programs/bay_delta/docs/cmnt091412/sldmwa/booth_et_al_2006.pdf Hydrologic Variability of the Cosumnes River Floodplain] (Booth et al., San Francisco Estuary and Watershed Science, Volume 4, Issue 2, 2006)</ref> or '''rolling mean''') is a calculation to analyze data points by creating a series of [[average]]s of different selections of the full data set. Variations include: [[#Simple moving average|simple]], [[#Cumulative moving average|cumulative]], or [[#Weighted moving average|weighted]] forms.

Mathematically, a moving average is a type of [[convolution]]. Thus in [[signal processing]] it is viewed as a [[low-pass filter|low-pass]] [[finite impulse response]] filter. Because the [[boxcar function]] outlines its filter coefficients, it is called a '''boxcar filter'''. It is sometimes followed by [[Downsampling (signal processing)|downsampling]].

Given a series of numbers and a fixed subset size, the first element of the moving average is obtained by taking the average of the initial fixed subset of the number series. Then the subset is modified by "shifting forward"; that is, excluding the first number of the series and including the next value in the series.

A moving average is commonly used with [[time series]] data to smooth out short-term fluctuations and highlight longer-term trends or cycles - in this case the calculation is sometimes called a '''time average'''. The threshold between short-term and long-term depends on the application, and the parameters of the moving average will be set accordingly. It is also used in [[economics]] to examine gross domestic product, employment or other macroeconomic time series. When used with non-time series data, a moving average filters higher frequency components without any specific connection to time, although typically some kind of ordering is implied. Viewed simplistically it can be regarded as smoothing the data.