Talk:Autocovariance

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autocorrelation

The previous suggestion that the autocovariance was the autocorrelation of a process with zero mean was just plain wrong. I thought this page could use extensive revision to bring it into line with the definition of covariance.

Richard Clegg

explain s

In

$C_{XX}(t,s)=cov(X_{t},X_{s})=E[(X_{t}-\mu _{t})(X_{s}-\mu _{s})]=E[X_{t}X_{s}]-\mu _{t}\mu _{s}.\,$

must explain what is s. --Krauss (talk) 07:42, 24 October 2014 (UTC)

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explain weakly stationary process

In If X(t) is a weakly stationary process, then the following are true:

$\mu _{t}=\mu _{s}=\mu \,$ for all t, s

and

$C_{XX}(t,s)=C_{XX}(s-t)=C_{XX}(\tau )\,$

where $\tau =|s-t|$ is the lag time, or the amount of time by which the signal has been shifted.

Please explain more about it.

$\mu _{t},\mu _{s},C_{XX}(t,s)\,$ and :$C_{XX}(s-t)\,$can not be found in link provided

--Kezhoulumelody (talk) 13:44, 26 April 2017 (UTC)

explain linearly filtered process

In The autocovariance of a linearly filtered process $Y_{t}$

$Y_{t}=\sum _{k=-\infty }^{\infty }a_{k}X_{t+k}\,$

is

$C_{YY}(\tau )=\sum _{k,l=-\infty }^{\infty }a_{k}a_{l}C_{XX}(\tau +k-l).\,$

Explain linearly filtered process and what properties the autocovariance will have if it is not a linearly filtered process.

--Kezhoulumelody (talk) 13:51, 26 April 2017 (UTC)