Wold decomposition
= Wold decomposition
{c}
{title2=$X_t=D_t+\sum_{j\ge0}c_j\epsilon_{t-j}$}
= Wold representation
{c}
{synonym}
A second-order stationary <time series> decomposes into a deterministic component and a one-sided square-summable <linear filter of a stationary time series> of its mutually orthogonal <linear innovations>. Normalize $c_0=1$. For a causal invertible <ARMA> process with no deterministic component, the driving <white noise> is this innovation process: observations and innovations span the same closed past subspace, while the next innovation is orthogonal to it.