Autocovariance vs. Covariance — What's the Difference?

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, covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the lesser values (that is, the variables tend to show similar behavior), the covariance is positive.

(statistics) The covariance of a signal with another part of the same signal

(Statistics) A statistical measure of the tendency of two random variables to vary in the same direction (called positive covariance) or in an opposite direction (called negative covariance) over many observations. Covariance is equal to the summed products of the deviations of corresponding values of the two variables from their respective means.

(Physics) The principle that the laws of physics have the same form regardless of the system of coordinates in which they are expressed.

(statistics) A statistical measure defined as $\backslash scriptstyle\backslash operatorname\{Cov\}(X,\; Y)\; =\; \backslash operatorname\{E\}((X\; -\; \backslash mu)\; (Y\; -\; \backslash nu))$ given two real-valued random variables X and Y, with expected values $\backslash scriptstyle\; E(X)\backslash ,=\backslash ,\backslash mu$ and $\backslash scriptstyle\; E(Y)\backslash ,=\backslash ,\backslash nu$.

(object-oriented programming) The conversion of data types from wider to narrower in certain situations.

A statistical measure of the relationship of two variables, formed by multiplying the difference of each variable from its mean, both variables being measured at the same time, and averaging all such products.

Statistical measure of the variance of two random variables measured in the same mean time period