Non-Stationary Stochastic Processes Estimation : : Vector Stationary Increments, Periodically Stationary Multi-Seasonal Increments / / Maksym Luz, Mikhail Moklyachuk.
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...
Saved in:
VerfasserIn: | |
---|---|
Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2024] ©2024 |
Year of Publication: | 2024 |
Language: | English |
Series: | De Gruyter Textbook
|
Online Access: | |
Physical Description: | 1 online resource (XVIII, 292 p.) |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
9783111325620 |
---|---|
ctrlnum |
(DE-B1597)661027 |
collection |
bib_alma |
record_format |
marc |
spelling |
Luz, Maksym, author. aut http://id.loc.gov/vocabulary/relators/aut Non-Stationary Stochastic Processes Estimation : Vector Stationary Increments, Periodically Stationary Multi-Seasonal Increments / Maksym Luz, Mikhail Moklyachuk. Berlin ; Boston : De Gruyter, [2024] ©2024 1 online resource (XVIII, 292 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda De Gruyter Textbook 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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 02. Jun 2024) Minimax Spektrale Eigenschaften. Prognose. Ungünstigste spektrale Dichte. minimax-robuste Schätzung. periodisch stationäre Inkremente. BUSINESS & ECONOMICS / Statistics. bisacsh Minimax-robust estimation, least favorable spectral density, minimax spectral characteristics, periodically stationary increments, forecasting. Moklyachuk, Mikhail, author. aut http://id.loc.gov/vocabulary/relators/aut EPUB 9783111326252 print 9783111325330 https://doi.org/10.1515/9783111325620 https://www.degruyter.com/isbn/9783111325620 Cover https://www.degruyter.com/document/cover/isbn/9783111325620/original |
language |
English |
format |
eBook |
author |
Luz, Maksym, Luz, Maksym, Moklyachuk, Mikhail, |
spellingShingle |
Luz, Maksym, Luz, Maksym, Moklyachuk, Mikhail, Non-Stationary Stochastic Processes Estimation : Vector Stationary Increments, Periodically Stationary Multi-Seasonal Increments / De Gruyter Textbook 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 |
author_facet |
Luz, Maksym, Luz, Maksym, Moklyachuk, Mikhail, Moklyachuk, Mikhail, Moklyachuk, Mikhail, |
author_variant |
m l ml m l ml m m mm |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Moklyachuk, Mikhail, Moklyachuk, Mikhail, |
author2_variant |
m m mm |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Luz, Maksym, |
title |
Non-Stationary Stochastic Processes Estimation : Vector Stationary Increments, Periodically Stationary Multi-Seasonal Increments / |
title_sub |
Vector Stationary Increments, Periodically Stationary Multi-Seasonal Increments / |
title_full |
Non-Stationary Stochastic Processes Estimation : Vector Stationary Increments, Periodically Stationary Multi-Seasonal Increments / Maksym Luz, Mikhail Moklyachuk. |
title_fullStr |
Non-Stationary Stochastic Processes Estimation : Vector Stationary Increments, Periodically Stationary Multi-Seasonal Increments / Maksym Luz, Mikhail Moklyachuk. |
title_full_unstemmed |
Non-Stationary Stochastic Processes Estimation : Vector Stationary Increments, Periodically Stationary Multi-Seasonal Increments / Maksym Luz, Mikhail Moklyachuk. |
title_auth |
Non-Stationary Stochastic Processes Estimation : Vector Stationary Increments, Periodically Stationary Multi-Seasonal Increments / |
title_alt |
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 |
title_new |
Non-Stationary Stochastic Processes Estimation : |
title_sort |
non-stationary stochastic processes estimation : vector stationary increments, periodically stationary multi-seasonal increments / |
series |
De Gruyter Textbook |
series2 |
De Gruyter Textbook |
publisher |
De Gruyter, |
publishDate |
2024 |
physical |
1 online resource (XVIII, 292 p.) 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 |
isbn |
9783111325620 9783111326252 9783111325330 |
url |
https://doi.org/10.1515/9783111325620 https://www.degruyter.com/isbn/9783111325620 https://www.degruyter.com/document/cover/isbn/9783111325620/original |
illustrated |
Not Illustrated |
doi_str_mv |
10.1515/9783111325620 |
work_keys_str_mv |
AT luzmaksym nonstationarystochasticprocessesestimationvectorstationaryincrementsperiodicallystationarymultiseasonalincrements AT moklyachukmikhail nonstationarystochasticprocessesestimationvectorstationaryincrementsperiodicallystationarymultiseasonalincrements |
status_str |
n |
ids_txt_mv |
(DE-B1597)661027 |
carrierType_str_mv |
cr |
is_hierarchy_title |
Non-Stationary Stochastic Processes Estimation : Vector Stationary Increments, Periodically Stationary Multi-Seasonal Increments / |
author2_original_writing_str_mv |
noLinkedField noLinkedField |
_version_ |
1806144938859036672 |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04950nam a2200685Ia 4500</leader><controlfield tag="001">9783111325620</controlfield><controlfield tag="003">DE-B1597</controlfield><controlfield tag="005">20240602123719.0</controlfield><controlfield tag="006">m|||||o||d||||||||</controlfield><controlfield tag="007">cr || ||||||||</controlfield><controlfield tag="008">240602t20242024gw fo d z eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783111325620</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9783111325620</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)661027</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-B1597</subfield><subfield code="b">eng</subfield><subfield code="c">DE-B1597</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">DE</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">BUS061000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Luz, Maksym, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Non-Stationary Stochastic Processes Estimation :</subfield><subfield code="b">Vector Stationary Increments, Periodically Stationary Multi-Seasonal Increments /</subfield><subfield code="c">Maksym Luz, Mikhail Moklyachuk.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin ;</subfield><subfield code="a">Boston : </subfield><subfield code="b">De Gruyter, </subfield><subfield code="c">[2024]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2024</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (XVIII, 292 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">text file</subfield><subfield code="b">PDF</subfield><subfield code="2">rda</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">De Gruyter Textbook</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Frontmatter -- </subfield><subfield code="t">Introduction -- </subfield><subfield code="t">Contents -- </subfield><subfield code="t">Notations and abbreviations -- </subfield><subfield code="t">1 Periodically stationary multi-seasonal increments of stochastic sequences -- </subfield><subfield code="t">2 Extrapolation of sequences with periodically stationary increments -- </subfield><subfield code="t">3 Extrapolation of sequences with periodically stationary increments observed with noise -- </subfield><subfield code="t">4 Interpolation of sequences with periodically stationary increments observed with or without noise -- </subfield><subfield code="t">5 Filtering of sequences with periodically stationary increments -- </subfield><subfield code="t">6 Continuous time stochastic processes with periodically correlated increments -- </subfield><subfield code="t">7 Extrapolation of processes with periodically correlated increments -- </subfield><subfield code="t">8 Extrapolation of processes with periodically correlated increments observed with noise -- </subfield><subfield code="t">9 Interpolation of processes with periodically correlated increments observed with or without noise -- </subfield><subfield code="t">10 Filtering of processes with periodically correlated increments -- </subfield><subfield code="t">11 Filtering problem when signal and noise have periodically correlated increments -- </subfield><subfield code="t">Problems -- </subfield><subfield code="t">A Some models of non-stationary time series -- </subfield><subfield code="t">Bibliography -- </subfield><subfield code="t">Index</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">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.</subfield></datafield><datafield tag="530" ind1=" " ind2=" "><subfield code="a">Issued also in print.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 02. Jun 2024)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Minimax Spektrale Eigenschaften.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Prognose.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ungünstigste spektrale Dichte.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">minimax-robuste Schätzung.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">periodisch stationäre Inkremente.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">BUSINESS & ECONOMICS / Statistics.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Minimax-robust estimation, least favorable spectral density, minimax spectral characteristics, periodically stationary increments, forecasting.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Moklyachuk, Mikhail, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">EPUB</subfield><subfield code="z">9783111326252</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">print</subfield><subfield code="z">9783111325330</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9783111325620</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.degruyter.com/isbn/9783111325620</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="3">Cover</subfield><subfield code="u">https://www.degruyter.com/document/cover/isbn/9783111325620/original</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_CL_LAEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_CL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_DGALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ECL_LAEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ECL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EEBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ESSHALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ESTMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_SSHALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_STMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV-deGruyter-alles</subfield></datafield></record></collection> |