View source for Auto-correlation

''of a stochastic process <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a013/a013940/a0139401.png" />''

[[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]]).



====Comments====
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" />.