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)