Talk:Autocovariance

WikiProject Statistics (Rated Start-class, Low-importance)

This article is within the scope of the WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page or join the discussion.

Start  This article has been rated as Start-Class on the quality scale.
Low  This article has been rated as Low-importance on the importance scale.

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

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

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

Hello fellow Wikipedians,

I have just modified one external link on Autocovariance. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at {{Sourcecheck}}).

An editor has reviewed this edit and fixed any errors that were found.

• If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
• If you found an error with any archives or the URLs themselves, you can fix them with this tool.

If you are unable to use these tools, you may set |needhelp=<your help request> on this template to request help from an experienced user. Please include details about your problem, to help other editors.

Cheers.—InternetArchiveBot 05:28, 22 October 2016 (UTC)

explain weakly stationary process

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

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

and

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

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

${\displaystyle \mu _{t},\mu _{s},C_{XX}(t,s)\,}$ and :${\displaystyle C_{XX}(s-t)\,}$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 ${\displaystyle Y_{t}}$

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

is

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

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)