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 can be written as the sum of two time series, one deterministic and one stochastic. Formally where: The moving average coefficients have these properties: 1. * Stable, that is square summable < 2. * Causal (i.e. there are no terms with j < 0) 3. * Minimum delay 4. * Constant ( independent of t) 5. * It is conventional to define

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 can be written as the sum of two time series, one deterministic and one stochastic. Formally where: The moving average coefficients have these properties: 1. * Stable, that is square summable < 2. * Causal (i.e. there are no terms with j < 0) 3. * Minimum delay 4. * Constant ( independent of t) 5. * It is conventional to define