Seasonal difference operator
= Seasonal difference operator
{title2=$\Delta_S=1-B^S$}
For an integer period $S$, $\Delta_SX_t=X_t-X_{t-S}$ uses the <backshift operator> as $1-B^S$. It annihilates a deterministic period-$S$ mean. If $X_t=m_t+\varepsilon_t$ with $m_{t+S}=m_t$ and <strong white noise>, the result is the stationary moving average $\varepsilon_t-\varepsilon_{t-S}$.