Autocovariance

s-th order autocovariance of $\{y_t\}$ is defined by the unconditional covariance of $y_t$ and $y_{t-s}$

$$cov(y_t,y_{t-s})=E\left[\right(y_t-E(y_t)\left)\right(y_{t-s}-E(y_{t-s})\left)\right]$$

Has to do with how a series is related to a lagged version to itself. Helps to find periodic patterns.

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References