The result of the previous example leads to the notion of causality which means that the process \((X_t: t\in\mathbb{Z})\) has a representation in terms of the white noise \((Z_s: s\leq t)\) and that ...The result of the previous example leads to the notion of causality which means that the process \((X_t: t\in\mathbb{Z})\) has a representation in terms of the white noise \((Z_s: s\leq t)\) and that is hence uncorrelated with the future as given by \((Z_s: s>t)\). It turns out that the characterization in terms of the zeroes of the autoregressive polynomials carries over from the AR(1) case to the general ARMA(\(p,q\)) case.
