Transitional surrogates

While an exact stationarization of a process with a given spectrum magnitude can be obtained via a complete randomization of the spectrum phase ("surrogates" technique), we pro pose here a softened version in which the degree of stationarization can be controlled by a perturbation of the actual phase. A basic theory for such "transitional surrogates" is first discussed, with emphasis on two effective constructions based on either white Gaussian noise or random walks. Some typical examples are considered for illustration, and performance evaluations are provided for supporting the usefulness of the approach in the context of stationarity testing.