Infinite moving-average representation
= Infinite moving-average representation
{title2=$X_t-\mu=\sum_{j\geq0}\psi_j\varepsilon_{t-j}$}
A causal square-integrable linear <time series> can be written $X_t=\mu+\sum_{j\geq0}\psi_j\varepsilon_{t-j}$. Square summability of the coefficients ensures mean-square convergence for <white noise>. An innovation representation additionally identifies its driving noise as the <innovation process>.