Wold Decomposition

In operator theory, a discipline within mathematics, the Wold decomposition, named after Herman Wold, or Wold–von Neumann decomposition, after Wold and John von Neumann, is a classification theorem for isometric linear operators on a given Hilbert space. It states that every isometry is a direct sums of copies of the unilateral shift and a unitary operator.

In time series analysis, the theorem implies that any stationary discrete-time stochastic process can be decomposed into a pair of uncorrelated processes, one deterministic, and the other being a moving average process.