Originally Posted by

**southprkfan1** Hi All, I have a question about using a back shift operator.

The Back shift operator B, is defined such that:

$\displaystyle B^{-1} E_t(X_t) = E_t(X_{t+1}) $

where $\displaystyle E_t $ is defined as the expectation given information at time t and X is a matrix.

My question is, what if we had something like the following:

$\displaystyle B^{-1}*A* E_t(X_t) $ for some constant matrix A. Would this equal

$\displaystyle A* E_t(X_{t+1}) $ or $\displaystyle A* E_t(X_t) $?