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A discrete time evolutionary second order process $X_t$ is
considered. Modulating functions that are the Fourier transform of
certain lattice distributions together with segments of a
stationary sequences are employed to form a process
$\widetilde{X}_t$. It is proved that
$\widetilde{X}_t\longrightarrow{X}_t$ in mean square, under
sufficient conditions. A formula in terms of the discrete Fourier
transform of a finite segment of the process, lattice weights and
the discrete Fourier transform of the stationary segment is
derived to estimate the stationary component of the spectral
density. Certain evolutionary ARMA processes are introduced that
can be used for the simulation.
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