Decomposition of stationary time series - finding the highly correlated components of stochastic processes
A stationary time series can be expressed by a sum of time series (components) occuring in a descending order of the magnitude of their autocorrelations. A few such components suffice for approximating the time series with a good accuracy. Since the first component is a highly correlated one, it is easier to work in applications. To perform the decomposition a particular optimization operator (optimator) with quadratic criterion called \(\zeta\)-optimator is introduced. The \(\zeta\)-optimator involves a shape parameter, so the decomposition is unique for any given value of that parameter. It is shown that in any decomposition the first component has a larger autocorrelation than the given i.e. original time series. Therefore weakly correlated processes can also involve highly correlated processes. Existence and uniqueness of the components is proved and some examples are worked out to illustrate the decomposition procedure.
scientific article; zbMATH DE number 4076390