What is Lag operator?

In time series analysis, the lag operator or backshift operator operates on an element of a time series to produce the previous element. For example, given some time series

then

or similarly in terms of the backshift operator B: B X t = X t − 1 {\displaystyle BX_{t}=X_{t-1}} for all t > 1 {\displaystyle t>1}. Equivalently, this definition can be represented as

The lag operator can be raised to arbitrary integer powers so that