A notation aid where the letter *B* denotes a backward shift of one period. Thus, *B* operating on *X*_{t}_{ }(noted as *BX*_{t}) yields, by definition, *X*_{t-}_{1}*. *Similarly *BB* or *B*^{2}* *is the same as shifting back by two periods. A first difference (*X*_{t}-X_{t-1}) for a time series can be denoted (1 – *B*)* X*_{t}. A second-order difference is denoted (1 – *B)*^{2} *X*_{t} . See differencing.