Estimates of functionals constructed from random sequences with periodically stationary increments

Kozak, P. S.; Moklyachuk, Mikhail

doi:10.1090/tpms/1050

Cited by 11 publications

(15 citation statements)

References 14 publications

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“…The following lemma and corollary describe representations of the functionals A ξ and A N ξ as sums of functionals with finite variances and functionals depending on the observed values of the sequence ξ(k) (see [18,20]).…”

Section: Hilbert Space Projection Methods Of Extrapolationmentioning

confidence: 99%

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Minimax prediction of sequences with periodically stationary increments

Kozak

Luz²,

Moklyachuk

2021

Carpathian Math. Publ.

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The problem of optimal estimation of linear functionals constructed from unobserved values of a stochastic sequence with periodically stationary increments based on its observations at points $ k<0$ is considered. 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 that determine the least favourable spectral densities and minimax (robust) spectral characteristics of the optimal linear estimates of functionals are derived in the case where spectral densities of the sequence are not exactly known while some sets of admissible spectral densities are given.

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Section: Hilbert Space Projection Methods Of Extrapolationmentioning

confidence: 99%

“…is the nth increment of the pth component of the vector-valued sequence ξ(m) (for more details see [18]).…”

Section: Definitionmentioning

confidence: 99%

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Minimax prediction of sequences with periodically stationary increments

Kozak

Luz²,

Moklyachuk

2021

Carpathian Math. Publ.

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“…and ⃗ c(k) = {c p (k)} T p=1 , k 0 are unknown coefficients to be found. Condition (29) implies the following representation of the spectral characteristic ⃗ h µ (λ)…”

Section: Forecasting Of Sequences With Periodically Stationary Seasonal Incrementsmentioning

confidence: 99%

“…We also mention works by Moklyachuk and Sidei [37,38], who derive minimax estimates of stationary processes from observations with missed values. Moklyachuk and Kozak [29] studied interpolation problem for stochastic sequences with periodically stationary increments.…”

Section: Introductionmentioning

confidence: 99%

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

Luz

Moklyachuk

2020

Stat., optim. inf. comput.

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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.

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References

2019

Estimation of Stochastic Processes With Stationary Increments and Cointegrated Sequences

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Estimates of functionals constructed from random sequences with periodically stationary increments

Cited by 11 publications

References 14 publications

Minimax prediction of sequences with periodically stationary increments

Minimax prediction of sequences with periodically stationary increments

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

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