Robust Filtering of Sequences with Periodically Stationary Multiplicative Seasonal Increments
نویسندگان
چکیده
We consider stochastic sequences with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally patterns. solve the filtering problem for linear functionals constructed from unobserved values a sequence this type based on observations noise sequence. For known matrices spectral densities, we obtain formulas calculating mean square errors characteristics optimal functionals. Formulas that determine least favourable densities minimax (robust) are proposed in case where not exactly while some sets admissible given.
منابع مشابه
Minimax-robust filtering problem for stochastic sequences with stationary increments and cointegrated sequences
The problem of optimal estimation of the linear functionals Aξ = ∑∞ k=0 a(k)ξ(−k) and AN ξ = ∑N k=0 a(k)ξ(−k) which depend on the unknown values of a stochastic sequence ξ(k) with stationary nth increments is considered. Estimates are based on observations of the sequence ξ(k) + η(k) at points of time k = 0,−1,−2, . . ., where the sequence η(k) is stationary and uncorrelated with the sequence ξ...
متن کاملMinimax-robust prediction problem for stochastic sequences with stationary increments and cointegrated sequences
The problem of optimal estimation of the linear functionals Aξ = ∑∞ k=0 a(k)ξ(k) and AN ξ = ∑N k=0 a(k)ξ(k) which depend on the unknown values of a stochastic sequence ξ(m) with stationary nth increments is considered. Estimates are obtained which are based on observations of the sequence ξ(m) + η(m) at points of time m = −1,−2, . . ., where the sequence η(m) is stationary and uncorrelated with...
متن کاملFiltering Problem for Functionals of Stationary Sequences
In this paper, we consider the problem of the mean-square optimal linear estimation of functionals which depend on the unknown values of a stationary stochastic sequence from observations with noise. In the case of spectral certainty in which the spectral densities of the sequences are exactly known, we propose formulas for calculating the spectral characteristic and value of the mean-square er...
متن کاملInterpolation of nonstationary fields with stationary increments
The problem of the linear interpolationof nonstationarymultidimensional processes with stationary increments is studied. The expressions of the interpolation filters and of the estimation error are derived, which generalize the results of the interpolation theory for stationary processes. Both finite and infinite extent interpolation are considered. An application to the interpolation of an und...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Statistics, Optimization and Information Computing
سال: 2021
ISSN: ['2310-5070', '2311-004X']
DOI: https://doi.org/10.19139/soic-2310-5070-1197