= Linear process
{disambiguate=time series}
{title2=$X_t=\mu+\sum_j\psi_j\varepsilon_{t-j}$}
= Linear process
{synonym}
A linear process is an L2-convergent white-noise filter $X_t=\mu+\sum_{j\in\mathbb Z}\psi_j\varepsilon_{t-j}$, with square-summable coefficients. It is weakly stationary, and its autocovariance is $\sigma_\varepsilon^2\sum_j\psi_j\psi_{j+h}$. A causal representation restricts the coefficients to $j\geq0$; it is then an <infinite moving-average representation>.
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