Autoregressive integrated moving average ($\varphi (B)(1-B{)}^d{X}_t=\vartheta (B){\epsilon }_t$)

An ARIMA model applies an autoregressive moving-average model to the differenced process $(1-B{)}^d{X}_t$, where $B$ is the backshift operator. Differencing permits stochastic trends whose levels are not weakly stationary processes. A local random-walk level observed with independent measurement white noise has an ARIMA(0,1,1) representation, or a formal ARMA(1,1) equation with autoregressive coefficient one.