In this note, we show that a stationary sequence obtained by applying a fixed deterministic function to shifts of a stationary sequence (satisfying a mild regularity condition) has a spectral density. In the multiparametric setting, we obtain a similar result for a function of a shifted i.i.d. field.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 441, 2015, pp. 274–285.
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Lifshits, M.A., Peligrad, M. On the Spectral Density of Stationary Processes and Random Fields. J Math Sci 219, 789–797 (2016). https://doi.org/10.1007/s10958-016-3147-9
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DOI: https://doi.org/10.1007/s10958-016-3147-9