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Maksym Luz^{1} and Mikhail Moklyachuk^{2
1}BNP Paribas Cardif, Kyiv, Ukraine

^{2}Taras Shevchenko National University of Kyiv, Ukraine

**Part of the Book: **Stochastic Processes: Fundamentals and Emerging Applications

We consider the problem of optimal estimation of linear functionals constructed from unobserved values of a stochastic sequence with periodically stationary increments based on observations of the sequence with a periodically stationary noise. For sequences with known spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of the functionals. Formulas defining the least favorable spectral densities and the minimax (robust) spectral characteristics of the optimal linear estimates of functionals are proposed in the case where the spectral densities of the sequences are not exactly known while some sets of admissible spectral densities are given.

**Keywords: **periodically stationary increments, PARIMA, minimax-robust estimate, least

favorable spectral density, minimax spectral characteristic

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