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Non-Stationary Stochastic Processes Estimation : Vector Stationary Increments, Periodically Stationary Multi-Seasonal Increments / Maksym Luz, Mikhail Moklyachuk.

By: Contributor(s): Material type: TextTextSeries: De Gruyter TextbookPublisher: Berlin ; Boston : De Gruyter, [2024]Copyright date: 2024Description: 1 online resource (XVIII, 292 p.)Content type:
Media type:
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ISBN:
  • 9783111325330
  • 9783111326252
  • 9783111325620
Subject(s): Other classification:
  • online - DeGruyter
Online resources: Available additional physical forms:
  • Issued also in print.
Contents:
Frontmatter -- Introduction -- Contents -- Notations and abbreviations -- 1 Periodically stationary multi-seasonal increments of stochastic sequences -- 2 Extrapolation of sequences with periodically stationary increments -- 3 Extrapolation of sequences with periodically stationary increments observed with noise -- 4 Interpolation of sequences with periodically stationary increments observed with or without noise -- 5 Filtering of sequences with periodically stationary increments -- 6 Continuous time stochastic processes with periodically correlated increments -- 7 Extrapolation of processes with periodically correlated increments -- 8 Extrapolation of processes with periodically correlated increments observed with noise -- 9 Interpolation of processes with periodically correlated increments observed with or without noise -- 10 Filtering of processes with periodically correlated increments -- 11 Filtering problem when signal and noise have periodically correlated increments -- Problems -- A Some models of non-stationary time series -- Bibliography -- Index
Summary: The problem of forecasting future values of economic and physical processes, the problem of restoring lost information, cleaning signals or other data observations from noise, is magnified in an information-laden word. Methods of stochastic processes estimation depend on two main factors. The first factor is construction of a model of the process being investigated. The second factor is the available information about the structure of the process under consideration. In this book, we propose results of the investigation of the problem of mean square optimal estimation (extrapolation, interpolation, and filtering) of linear functionals depending on unobserved values of stochastic sequences and processes with periodically stationary and long memory multiplicative seasonal increments. Formulas for calculating the mean square errors and the spectral characteristics of the optimal estimates of the functionals are derived in the case of spectral certainty, where spectral structure of the considered sequences and processes are exactly known. In the case where spectral densities of the sequences and processes are not known exactly while some sets of admissible spectral densities are given, we apply the minimax-robust method of estimation.
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Item type Current library Call number URL Status Notes Barcode
eBook eBook Biblioteca "Angelicum" Pont. Univ. S.Tommaso d'Aquino Nuvola online online - DeGruyter (Browse shelf(Opens below)) Online access Not for loan (Accesso limitato) Accesso per gli utenti autorizzati / Access for authorized users (dgr)9783111325620

Frontmatter -- Introduction -- Contents -- Notations and abbreviations -- 1 Periodically stationary multi-seasonal increments of stochastic sequences -- 2 Extrapolation of sequences with periodically stationary increments -- 3 Extrapolation of sequences with periodically stationary increments observed with noise -- 4 Interpolation of sequences with periodically stationary increments observed with or without noise -- 5 Filtering of sequences with periodically stationary increments -- 6 Continuous time stochastic processes with periodically correlated increments -- 7 Extrapolation of processes with periodically correlated increments -- 8 Extrapolation of processes with periodically correlated increments observed with noise -- 9 Interpolation of processes with periodically correlated increments observed with or without noise -- 10 Filtering of processes with periodically correlated increments -- 11 Filtering problem when signal and noise have periodically correlated increments -- Problems -- A Some models of non-stationary time series -- Bibliography -- Index

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http://purl.org/coar/access_right/c_16ec

The problem of forecasting future values of economic and physical processes, the problem of restoring lost information, cleaning signals or other data observations from noise, is magnified in an information-laden word. Methods of stochastic processes estimation depend on two main factors. The first factor is construction of a model of the process being investigated. The second factor is the available information about the structure of the process under consideration. In this book, we propose results of the investigation of the problem of mean square optimal estimation (extrapolation, interpolation, and filtering) of linear functionals depending on unobserved values of stochastic sequences and processes with periodically stationary and long memory multiplicative seasonal increments. Formulas for calculating the mean square errors and the spectral characteristics of the optimal estimates of the functionals are derived in the case of spectral certainty, where spectral structure of the considered sequences and processes are exactly known. In the case where spectral densities of the sequences and processes are not known exactly while some sets of admissible spectral densities are given, we apply the minimax-robust method of estimation.

Issued also in print.

Mode of access: Internet via World Wide Web.

In English.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 20. Nov 2024)