Wold's theorem
In statistics, Wold's decomposition or the Wold representation theorem (not to be confused with the Wold theorem that is the discrete-time analog of the Wiener–Khinchin theorem), named after Herman Wold, says that every covariance-stationary time series Y t {\displaystyle Y_{t}} can be written as the sum of two time series, one deterministic and one stochastic. Formally Y t = ∑ j = 0 ∞ b j ε t − j + η t , {\displaystyle Y_{t}=\sum _{j=0}^{\infty }b_{j}\varepsilon _{t-j}+\eta _{t},} where: Y t {\displaystyle Y_{t}} is the time series being considered, ε t {\displaystyle \varepsilon _{t}} is an uncorrelated sequence which is the innovation process to the process Y t {\displaystyle Y_{t}} – that is, a white noise process that is input to the linear filter { b j } {\displaystyle \{b_{j}\}} .