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We introduce stochastic sequences $\zeta(k)$ with periodically stationarygeneralized multiple increments of fractional order which combinescyclostationary, multi-seasonal, integrated and fractionally integratedpatterns. We solve the problem of optimal estimation of linear functionalsconstructed from unobserved values of stochastic sequences $\zeta(k)$ based ontheir observations at points $ k<0$. For sequences with known spectraldensities, we obtain formulas for calculating values of the mean square errorsand the spectral characteristics of the optimal estimates of functionals.Formulas that determine the least favorable spectral densities and minimax(robust) spectral characteristics of the optimal linear estimates offunctionals are proposed in the case where spectral densities of sequences arenot exactly known while some sets of admissible spectral densities are given.

Minimax-robust forecasting of sequences with periodically stationary long memory multiple seasonal increments