Robust filtering of sequences with periodically stationary multiplicative seasonal increments
Анотація
We study stochastic sequences $ξ(k)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the filtering problem for linear functionals constructed from unobserved values of a stochastic sequence $ξ(k)$ based on observations with the periodically stationary noise sequence. 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 sequences are not exactly known while some sets of admissible spectral densities are given.
Класифікація
Ідентифікатори
Рецензії (0)
Написати рецензіюРецензій ще немає. Будьте першим!
Схожі роботи
Asymptotic Properties of Drift Parameter Estimator Based on Discrete Observations of Stochastic Differential Equation Driven by Fractional Brownian Motion
Схоже за: Stochastic processes and financial applications · Financial Risk and Volatility Modeling
Approximation of multifractional Brownian motion by absolutely continuous processes
Схоже за: Stochastic processes and financial applications · Financial Risk and Volatility Modeling
Asymptotic Growth of Sample Paths of Tempered Fractional Brownian Motions, with Statistical Applications to Vasicek-Type Models
Схоже за: Stochastic processes and financial applications · Financial Risk and Volatility Modeling
Optimization of small deviation for mixed fractional Brownian motion with trend
Схоже за: Stochastic processes and financial applications · Financial Risk and Volatility Modeling
Generalized Peano problem with Lévy noise
Схоже за: Stochastic processes and financial applications · Financial Risk and Volatility Modeling
An estimate of the rate of convergence of an approximating scheme applied to a stochastic differential equation with an additional parameter
Схоже за: Stochastic processes and financial applications · Financial Risk and Volatility Modeling