Non-stationary stochastic processes estimation: vector stationary increments, periodically stationary multi-seasonal increments
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:
| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2024]
© 2024 |
| Series: | De Gruyter Textbook
|
| Subjects: | |
| Online Access: | DE-1043 DE-1046 DE-858 DE-898 DE-859 DE-860 DE-91 DE-473 DE-703 DE-20 DE-739 Volltext |
| 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 |
| Physical Description: | 1 Online-Ressource (XVIII, 292 Seiten) |
| ISBN: | 9783111325620 9783111326252 |
| DOI: | 10.1515/9783111325620 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV049730686 | ||
| 003 | DE-604 | ||
| 005 | 20250402 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 240605s2024 xx o|||| 00||| eng d | ||
| 020 | |a 9783111325620 |c Online; PDF |9 978-3-11-132562-0 | ||
| 020 | |a 9783111326252 |c Online, EPUB |9 978-3-11-132625-2 | ||
| 024 | 7 | |a 10.1515/9783111325620 |2 doi | |
| 035 | |a (ZDB-23-DGG)9783111325620 | ||
| 035 | |a (OCoLC)1437883684 | ||
| 035 | |a (DE-599)BVBBV049730686 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1043 |a DE-1046 |a DE-858 |a DE-859 |a DE-860 |a DE-473 |a DE-739 |a DE-703 |a DE-11 |a DE-91 |a DE-898 |a DE-20 | ||
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Luz, Maksym |e Verfasser |0 (DE-588)134106686X |4 aut | |
| 245 | 1 | 0 | |a Non-stationary stochastic processes estimation |b vector stationary increments, periodically stationary multi-seasonal increments |c Maksym Luz, Mikhail Moklyachuk |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2024] | |
| 264 | 1 | |c © 2024 | |
| 300 | |a 1 Online-Ressource (XVIII, 292 Seiten) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter Textbook | |
| 520 | |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 | ||
| 650 | 4 | |a Minimax Spektrale Eigenschaften | |
| 650 | 4 | |a Prognose | |
| 650 | 4 | |a Ungünstigste spektrale Dichte | |
| 650 | 4 | |a minimax-robuste Schätzung | |
| 650 | 4 | |a periodisch stationäre Inkremente | |
| 650 | 7 | |a BUSINESS & ECONOMICS / Statistics |2 bisacsh | |
| 700 | 1 | |a Moklyachuk, Mikhail |e Verfasser |0 (DE-588)1306178401 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-3-11-132533-0 |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9783111325620 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-23-DGG | ||
| 912 | |a ZDB-23-DMA | ||
| 940 | 1 | |q ZDB-23-DMA24 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035072887 | |
| 966 | e | |u https://doi.org/10.1515/9783111325620 |l DE-1043 |p ZDB-23-DGG |q FAB_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783111325620 |l DE-1046 |p ZDB-23-DGG |q FAW_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783111325620 |l DE-858 |p ZDB-23-DGG |q FCO_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783111325620 |l DE-898 |p ZDB-23-DMA |q ZDB-23-DMA24 |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783111325620 |l DE-859 |p ZDB-23-DGG |q FKE_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783111325620 |l DE-860 |p ZDB-23-DGG |q FLA_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783111325620 |l DE-91 |p ZDB-23-DMA |q TUM_Paketkauf_2024 |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783111325620 |l DE-473 |p ZDB-23-DGG |q UBG_PDA_DGG |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783111325620 |l DE-703 |p ZDB-23-DMA |q ZDB-23-DMA24 |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783111325620 |l DE-20 |p ZDB-23-DMA |q UBW_Paketkauf |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1515/9783111325620 |l DE-739 |p ZDB-23-DGG |q UPA_PDA_DGG |x Verlag |3 Volltext | |
Record in the Search Index
| _version_ | 1828277021195632640 |
|---|---|
| adam_text | |
| any_adam_object | |
| author | Luz, Maksym Moklyachuk, Mikhail |
| author_GND | (DE-588)134106686X (DE-588)1306178401 |
| author_facet | Luz, Maksym Moklyachuk, Mikhail |
| author_role | aut aut |
| author_sort | Luz, Maksym |
| author_variant | m l ml m m mm |
| building | Verbundindex |
| bvnumber | BV049730686 |
| classification_tum | MAT 000 |
| collection | ZDB-23-DGG ZDB-23-DMA |
| ctrlnum | (ZDB-23-DGG)9783111325620 (OCoLC)1437883684 (DE-599)BVBBV049730686 |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9783111325620 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 c 4500</leader><controlfield tag="001">BV049730686</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20250402</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">240605s2024 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783111325620</subfield><subfield code="c">Online; PDF</subfield><subfield code="9">978-3-11-132562-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783111326252</subfield><subfield code="c">Online, EPUB</subfield><subfield code="9">978-3-11-132625-2</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">(ZDB-23-DGG)9783111325620</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1437883684</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV049730686</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-1043</subfield><subfield code="a">DE-1046</subfield><subfield code="a">DE-858</subfield><subfield code="a">DE-859</subfield><subfield code="a">DE-860</subfield><subfield code="a">DE-473</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-898</subfield><subfield code="a">DE-20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Luz, Maksym</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)134106686X</subfield><subfield code="4">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 ; Boston</subfield><subfield code="b">De Gruyter</subfield><subfield code="c">[2024]</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">© 2024</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XVIII, 292 Seiten)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">De Gruyter Textbook</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="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="700" ind1="1" ind2=" "><subfield code="a">Moklyachuk, Mikhail</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1306178401</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-3-11-132533-0</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9783111325620</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DGG</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DMA</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-23-DMA24</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-035072887</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783111325620</subfield><subfield code="l">DE-1043</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FAB_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783111325620</subfield><subfield code="l">DE-1046</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FAW_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783111325620</subfield><subfield code="l">DE-858</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FCO_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783111325620</subfield><subfield code="l">DE-898</subfield><subfield code="p">ZDB-23-DMA</subfield><subfield code="q">ZDB-23-DMA24</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783111325620</subfield><subfield code="l">DE-859</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FKE_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783111325620</subfield><subfield code="l">DE-860</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">FLA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783111325620</subfield><subfield code="l">DE-91</subfield><subfield code="p">ZDB-23-DMA</subfield><subfield code="q">TUM_Paketkauf_2024</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783111325620</subfield><subfield code="l">DE-473</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">UBG_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783111325620</subfield><subfield code="l">DE-703</subfield><subfield code="p">ZDB-23-DMA</subfield><subfield code="q">ZDB-23-DMA24</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783111325620</subfield><subfield code="l">DE-20</subfield><subfield code="p">ZDB-23-DMA</subfield><subfield code="q">UBW_Paketkauf</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1515/9783111325620</subfield><subfield code="l">DE-739</subfield><subfield code="p">ZDB-23-DGG</subfield><subfield code="q">UPA_PDA_DGG</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV049730686 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-02T08:00:38Z |
| institution | BVB |
| isbn | 9783111325620 9783111326252 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035072887 |
| oclc_num | 1437883684 |
| open_access_boolean | |
| owner | DE-1043 DE-1046 DE-858 DE-859 DE-860 DE-473 DE-BY-UBG DE-739 DE-703 DE-11 DE-91 DE-BY-TUM DE-898 DE-BY-UBR DE-20 |
| owner_facet | DE-1043 DE-1046 DE-858 DE-859 DE-860 DE-473 DE-BY-UBG DE-739 DE-703 DE-11 DE-91 DE-BY-TUM DE-898 DE-BY-UBR DE-20 |
| physical | 1 Online-Ressource (XVIII, 292 Seiten) |
| psigel | ZDB-23-DGG ZDB-23-DMA ZDB-23-DMA24 ZDB-23-DGG FAB_PDA_DGG ZDB-23-DGG FAW_PDA_DGG ZDB-23-DGG FCO_PDA_DGG ZDB-23-DMA ZDB-23-DMA24 ZDB-23-DGG FKE_PDA_DGG ZDB-23-DGG FLA_PDA_DGG ZDB-23-DMA TUM_Paketkauf_2024 ZDB-23-DGG UBG_PDA_DGG ZDB-23-DMA UBW_Paketkauf ZDB-23-DGG UPA_PDA_DGG |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter Textbook |
| spelling | Luz, Maksym Verfasser (DE-588)134106686X 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-Ressource (XVIII, 292 Seiten) txt rdacontent c rdamedia cr rdacarrier De Gruyter Textbook 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 Minimax Spektrale Eigenschaften Prognose Ungünstigste spektrale Dichte minimax-robuste Schätzung periodisch stationäre Inkremente BUSINESS & ECONOMICS / Statistics bisacsh Moklyachuk, Mikhail Verfasser (DE-588)1306178401 aut Erscheint auch als Druck-Ausgabe 978-3-11-132533-0 https://doi.org/10.1515/9783111325620 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Luz, Maksym Moklyachuk, Mikhail Non-stationary stochastic processes estimation vector stationary increments, periodically stationary multi-seasonal increments Minimax Spektrale Eigenschaften Prognose Ungünstigste spektrale Dichte minimax-robuste Schätzung periodisch stationäre Inkremente BUSINESS & ECONOMICS / Statistics bisacsh |
| title | Non-stationary stochastic processes estimation vector stationary increments, periodically stationary multi-seasonal increments |
| title_auth | Non-stationary stochastic processes estimation vector stationary increments, periodically stationary multi-seasonal increments |
| title_exact_search | Non-stationary stochastic processes estimation 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_short | Non-stationary stochastic processes estimation |
| title_sort | non stationary stochastic processes estimation vector stationary increments periodically stationary multi seasonal increments |
| title_sub | vector stationary increments, periodically stationary multi-seasonal increments |
| topic | Minimax Spektrale Eigenschaften Prognose Ungünstigste spektrale Dichte minimax-robuste Schätzung periodisch stationäre Inkremente BUSINESS & ECONOMICS / Statistics bisacsh |
| topic_facet | Minimax Spektrale Eigenschaften Prognose Ungünstigste spektrale Dichte minimax-robuste Schätzung periodisch stationäre Inkremente BUSINESS & ECONOMICS / Statistics |
| url | https://doi.org/10.1515/9783111325620 |
| work_keys_str_mv | AT luzmaksym nonstationarystochasticprocessesestimationvectorstationaryincrementsperiodicallystationarymultiseasonalincrements AT moklyachukmikhail nonstationarystochasticprocessesestimationvectorstationaryincrementsperiodicallystationarymultiseasonalincrements |