Wold's Theorem

Wold’s Decomposition Theorem states that any weakly stationary process, $Y_t$, can be written as:

$Y_t = D_t + \sum_{j=0}^{\infty} \psi_j \varepsilon_{t-j}$

• $D_t$ is deterministic (here taken to have zero mean).
• The stochastic term is an MA($\infty$) in innovations $\varepsilon_t$.
• $\psi_0=1$ and $\sum_{j\ge 0}\psi_j^2<\infty$.