Editing Moving average (section)

=={{anchor|Exponential}}Exponential moving average==
{{main|Exponential smoothing}}
{{further|EWMA chart}}
An '''exponential moving average (EMA)''', also known as an '''exponentially weighted moving average (EWMA)''',<ref>{{cite web |url=http://lorien.ncl.ac.uk/ming/filter/filewma.htm |title=DEALING WITH MEASUREMENT NOISE - Averaging Filter |access-date=2010-10-26 |url-status=dead |archive-url=https://web.archive.org/web/20100329135531/http://lorien.ncl.ac.uk/ming/filter/filewma.htm |archive-date=2010-03-29 }}</ref> is a first-order [[infinite impulse response]] filter that applies weighting factors which decrease [[Exponential decay|exponentially]]. The weighting for each older [[data|datum]] decreases exponentially, never reaching zero. 
This formulation is according to Hunter (1986).<ref>[http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc431.htm NIST/SEMATECH e-Handbook of Statistical Methods: Single Exponential Smoothing] at the [[National Institute of Standards and Technology]]</ref>

There is also a multivariate implementation of EWMA, known as MEWMA.<ref>{{cite journal |last1=Yeh |first1=A. |last2=Lin |first2=D. |last3=Zhou |first3=H. |last4=Venkataramani |first4=C. |title=A multivariate exponentially weighted moving average control chart for monitoring process variability |journal=[[Journal of Applied Statistics]] |date=2003 |volume=30 |issue=5 |pages=507–536 |doi=10.1080/0266476032000053655 |bibcode=2003JApSt..30..507Y |url=https://www.stat.purdue.edu/~dkjlin/documents/publications/2003/2003_AppStat1.pdf |access-date=16 January 2025 |issn=0266-4763}}</ref>