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Difference between revisions of "Auto-correlation"

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''of a stochastic process <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013940/a0139401.png" />''
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[[Correlation|Correlation]] of the values of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013940/a0139402.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013940/a0139403.png" />. The term  "auto-correlation" , along with the term  "correlation function" , is mostly employed in studies of stationary stochastic processes, in which the auto-correlation depends only on <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013940/a0139404.png" /> and not on <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013940/a0139405.png" /> (cf. [[Stationary stochastic process|Stationary stochastic process]]).
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''of a stochastic process $X_t$''
  
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Correlation of the values of $X_t$ and $X_{t+h}$. The term  "auto-correlation" , along with the term  "correlation function" , is mostly employed in studies of [[stationary stochastic process]]es, in which the auto-correlation depends only on $h$ and not on $t$.
  
  
 
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I.e. the auto-correlation of the process <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013940/a0139406.png" /> is the [[Correlation coefficient|correlation coefficient]] of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013940/a0139407.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013940/a0139408.png" />.
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I.e. the auto-correlation of the process $X_t$ is the [[correlation coefficient]] of $X_t$ and $X_{t+h}$.
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Latest revision as of 18:01, 10 January 2016

2020 Mathematics Subject Classification: Primary: 60G [MSN][ZBL]

of a stochastic process $X_t$

Correlation of the values of $X_t$ and $X_{t+h}$. The term "auto-correlation" , along with the term "correlation function" , is mostly employed in studies of stationary stochastic processes, in which the auto-correlation depends only on $h$ and not on $t$.


Comments

I.e. the auto-correlation of the process $X_t$ is the correlation coefficient of $X_t$ and $X_{t+h}$.

How to Cite This Entry:
Auto-correlation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Auto-correlation&oldid=15589
This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article