= Autoregressive integrated moving average
{title2=$\phi(B)(1-B)^dX_t=\vartheta(B)\varepsilon_t$}
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= Autoregressive integrated moving-average model
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= ARIMA
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{synonym}
An <ARIMA> model applies an <autoregressive moving-average model> to the differenced process $(1-B)^dX_t$, 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.
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