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We consider a stochastic sequence $\xi(m)$ with periodically stationarygeneralized multiple increments of fractional order which combinescyclostationary, multi-seasonal, integrated and fractionally integratedpatterns. The filtering problem is solved for this type of sequences based onobservations with a periodically stationary noise. When spectral densities areknown and allow the canonical factorizations, we derive the mean square errorand the spectral characteristics of the optimal estimate of the functional$A{\xi}=\sum_{k=0}^{\infty}{a}(k) {\xi}(-k)$. Formulas that determine the leastfavourable spectral densities and the minimax (robust) spectral characteristicsof the optimal linear estimate of the functional are proposed in the case wherethe spectral densities are not known, but some sets of admissible spectraldensities are given.

Filtering problem for sequences with periodically stationary multiseasonal increments with spectral densities allowing canonical factorizations