TY - JOUR
AU - Maksym Luz
AU - Mikhail Moklyachuk
PY - 2020/07/25
Y2 - 2020/09/29
TI - Minimax-robust forecasting of sequences with periodically stationary long memory multiple seasonal increments
JF - Statistics, Optimization & Information Computing
JA - Stat., optim. inf. comput.
VL - 8
IS - 3
SE - Research Articles
DO - 10.19139/soic-2310-5070-998
UR - http://iapress.org/index.php/soic/article/view/998
AB - We introduce a stochastic sequence $\zeta(k)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the problem of optimal estimation of linear functionals constructed from unobserved values of the stochastic sequence $\zeta(k)$ based on its observations at points $ k<0$. For sequences with known matrices of 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 that determine the least favorable spectral densities and minimax (robust) spectral characteristics of the optimal linear estimates of the functionals are proposed in the case where spectral densities of the sequence are not exactly known while some sets of admissible spectral densities are given.
ER -