Cross covariance

In probability and statistics, given two ${\displaystyle X=(X_{t})}$ and ${\displaystyle Y=(Y_{t})}$, the cross-covariance is a function that gives the covariance of one process with the other at pairs of time points. With the usual notation E  for the expectation operator, if the processes have the mean functions ${\displaystyle \mu _{t}=E[X_{t}]}$ and ${\displaystyle \nu _{t}=E[Y_{t}]}$, then the cross-covariance is given by

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