Wold's Theorem
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High Quality Content by WIKIPEDIA articles! In statistics, Wold's theorem or Wold representation theorem, named after Herman Wold, says that every covariance-stationary time series Yt can be written as an infinite moving average (MA(infty)) process of its innovation process. Such a formulation is known as a moving average representation for the time series. This is also known as the Wold decomposition theorem. The usefulness of the Wold Theorem is that it allows the dynamic evolution of a variable Yt to be approximated by a linear model. If the innovations varepsilon_{t} are independent, then ...
High Quality Content by WIKIPEDIA articles! In statistics, Wold's theorem or Wold representation theorem, named after Herman Wold, says that every covariance-stationary time series Yt can be written as an infinite moving average (MA(infty)) process of its innovation process. Such a formulation is known as a moving average representation for the time series. This is also known as the Wold decomposition theorem. The usefulness of the Wold Theorem is that it allows the dynamic evolution of a variable Yt to be approximated by a linear model. If the innovations varepsilon_{t} are independent, then the linear model is the only possible representation relating the observed value of Yt to its past evolution. However, when varepsilon_{t} is merely an uncorrelated but not independent sequence, then the linear model exists but it is not the only representation of the dynamic dependence of the series. In this latter case, it is possible that the linear model may not be very useful, and therewould be a nonlinear model relating the observed value of Yt to its past evolution.
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