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UID:

Umfang: 1 online resource (XVIII, 292 p.)

ISBN: 9783111325620

Serie: De Gruyter Textbook

Inhalt: 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.

Anmerkung: 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 , Issued also in print. , In English.

Weitere Ausg.: ISBN 9783111326252

Weitere Ausg.: ISBN 9783111325330

Sprache: Englisch

DOI: 10.1515/9783111325620

URL: https://doi.org/10.1515/9783111325620

URL: https://www.degruyter.com/isbn/9783111325620

URL: https://doi.org/10.1515/9783111325620

URL: https://www.degruyter.com/isbn/9783111325620

URL: Volltext  (URL des Erstveröffentlichers)

URL: lizenzpflichtig

URL: lizenzpflichtig

URL: Cover

UID:

Umfang: 1 Online-Ressource (XVIII, 292 p.)

Ausgabe: Reproduktion Issued also in print

ISBN: 9783111325620

Serie: De Gruyter Textbook

Inhalt: 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

Anmerkung: 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 , Issued also in print , In English

Weitere Ausg.: ISBN 9783111326252

Weitere Ausg.: ISBN 9783111325330

Weitere Ausg.: Erscheint auch als print ISBN 9783111325330

Weitere Ausg.: Erscheint auch als Druck-Ausgabe Luz, Maksym Non-stationary stochastic processes estimation Berlin : De Gruyter, 2024 ISBN 9783111325330

Weitere Ausg.: ISBN 3111325334

Sprache: Englisch

DOI: 10.1515/9783111325620

URL: lizenzpflichtig

URL: lizenzpflichtig

URL: Cover

UID:

Umfang: XVIII, 292 Seiten , 24 cm x 17 cm, 514 g

Ausgabe: 1

ISBN: 9783111325330 , 3111325334

Serie: De Gruyter Graduate

Anmerkung: Erscheint auch als Online-Ausgabe 9783111326252 (ISBN)

Sprache: Englisch

URL: https://www.degruyter.com/isbn/9783111325330

URL: https://d-nb.info/1321018126/04