In probability theory and statistics, given a stochastic process, the autocovariance is a function that gives the covariance of the process with itself at pairs of time points. Autocovariance is closely related to the autocorrelation of the process in question.
In probability theory and statistics, given a stochastic process, the autocovariance is a function that gives the covariance of the process with itself at pairs of time points. Autocovariance is closely related to the autocorrelation of the process in question.
== Auto-covariance of stochastic processes == === Definition === With the usual notation \operatorname{E} for the expectation operator, if the stochastic process \left\{X_t\right\} has the mean function \mu_t = \operatorname{E}[X_t], then the autocovariance is given by {{Equation box 1 |indent = : |title= |equation = {{NumBlk||\operatorname{K}_{XX}(t_1,t_2) = \operatorname{cov}\left[X_{t_1}, X_{t_2}\right] = \operatorname{E}[(X_{t_1} - \mu_{t_1})(X_{t_2} - \mu_{t_2})] = \operatorname{E}[X_{t_1} X_{t_2}] - \mu_{t_1} \mu_{t_2}|}} |cellpadding= 6 |border |border colour = #0073CF |background colour=#F5FFFA}} where t_1 and t_2 are two instances in time.
Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).