 Linear process (time series)

A linear process is an L2-convergent white-noise filter $X_t=\mu +{\sum }_{j\in \mathbb{Z}}{\psi }_j{\epsilon }_{t-j}$, with square-summable coefficients. It is weakly stationary, and its autocovariance is ${\sigma }_{\epsilon }^2{\sum }_j{\psi }_j{\psi }_{j+h}$. A causal representation restricts the coefficients to $j\ge 0$; it is then an infinite moving-average representation.