Asymptotic change-point analysis of the dependencies in time series:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Köln
23. Mai 2016
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 185 Seiten Illustrationen |
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| 245 | 1 | 0 | |a Asymptotic change-point analysis of the dependencies in time series |c vorgelegt von Christoph Heuser |
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Record in the Search Index
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| adam_text | Titel: Asymptotic change-point analysis of the dependencies in time series
Autor: Heuser, Christoph
Jahr: 2016
Contents
1 Introduction 2
1.1 Introduction.......................................... 2
1.2 Main Model and its Assumptions.............................. 3
1.3 Test Statistics and Stopping Times............................. 6
2 Change-Point Analysis of the Correlations under Known Means and Variances 9
2.1 A Posteriori Analysis under General Dependency Framework.............. 9
2.1.1 Testing under a Functional Central Limit Theorem................................9
2.1.2 Change-Point Estimation............................................................16
2.1.3 Long-run Variance Estimation ......................................................26
2.2 Sequential Analysis under General Dependency Framework..............................28
2.2.1 Closed-end Procedure................................................................28
2.2.2 Open-end Procedure..................................................................30
2.3 Examples......................................................................................35
2.3.1 Identical Independent Distribution..................................................35
2.3.2 Mixing ................................................................................38
2.3.3 Near Epoch Dependent ..............................................................39
2.3.4 Time Series............................................................................42
3 Assumptions on the Unknown Means and Variances 44
3.1 Assumptions in the a Posteriori Analysis....................................................44
3.2 Assumptions in the Sequential Analysis....................................................48
4 Change-Point Analysis of the Correlation under Unknown Means and Known Vari-
ances 50
4.1 A Posteriori Analysis under a General Dependency Framework and General Mean Es-
timates ........................................................................................50
4.1.1 Testing under a Functional Central Limit Theorem and Unknown Means ... 50
4.1.2 Change-Point Estimation under Unknown Means..................................57
4.1.3 Long-run Variance Estimation under Unknown Means............................69
4.2 Sequential Analysis under a General Dependency Framework and General Mean Estimates 75
4.2.1 Closed-end Procedure under Unknown Means......................................75
4.2.2 Open-end under Unknown Means....................................................79
4.3 Examples......................................................................................82
4.3.1 Constant Means......................................................................82
4.3.2 Non-constant Means..................................................................83
5 Change-Point Analysis of the Correlation under Known Means and Unknown Vari-
ances 90
5.1 A Posteriori Analysis under a General Dependency Framework and General Variance
Estimates......................................................................................90
5.1.1 Testing under a Functional Central Limit Theorem and General Variance Esti-
mates ..................................................................................90
5.1.2 Change-Point Estimation under Unknown Variances..............................97
5.1.3 Long-run Variance Estimation under Unknown Variances........................100
5.2 Sequential Analysis under a General Dependency Framework and General Variance
Estimates......................................................................................106
5.2.1 Closed-end Procedure under Unknown Variances..................................106
5.2.2 Open-end Procedure under Unknown Variances....................................110
5.3 Examples......................................................................................112
5.3.1 Constant Variances....................................................................112
5.3.2 Non-constant Variances..............................................................113
6 Change-Point Analysis of the Correlation under Unknown Means and Variances 116
6.1 A Posteriori Analysis under a General Dependency Framework, General Mean and
Variance Estimates............................................................................116
6.1.1 Testing under a Functional Central Limit Theorem, General Mean and Variance
Estimates..............................................................................116
6.1.2 Change-Point Estimation under Unknown Means and Variances.........118
6.1.3 Long-run Variance Estimation under Unknown Means and Variances......120
6.2 Sequential Analysis under General Dependency Framework and General Variance and
Mean Estimates................................................................................123
6.2.1 Closed-end Procedure with Unknown Means and Variances...........123
6.2.2 Open-end with Unknown Means and Variances....................................124
6.3 Examples...........................................126
6.3.1 Constant Parameters..................................................................126
6.3.2 Non-constant Parameters............................................................127
7 Simulation Study 128
7.1 A Posteriori Testing..........................................................................128
7.1.1 Influence of the Mean Estimates under Ho..........................................130
7.1.2 Influence of the Variance Estimates under Ho ....................................136
7.1.3 Influence of the Combination of Mean and Variance Estimates under Ho ¦¦ ¦ 140
7.1.4 Asymptotic Power........... ..............................................143
7.2 Sequential Analysis............................................................................150
7.2.1 Influence of the Mean Estimates under H^ ......................................152
7.2.2 Influence of the Variance Estimates under H^ and Known Means......154
7.2.3 Influence of the Combination of Mean and Variance Estimates under Hq2 . . 156
7.2.4 Stopping behavior under some Alternatives........................................157
7.3 Change-Point Estimation ............................................................Ig5
7.4 Real Data Application............................................................171
A Proofs of Section 2 173
B Lemmas for the Main Results
178
|
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| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| spelling | Heuser, Christoph Verfasser (DE-588)1105594327 aut Asymptotic change-point analysis of the dependencies in time series vorgelegt von Christoph Heuser Köln 23. Mai 2016 185 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Dissertation Universität zu Köln 2016 Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Change-point-Problem (DE-588)4598971-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Zeitreihenanalyse (DE-588)4067486-1 s Change-point-Problem (DE-588)4598971-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029421435&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Heuser, Christoph Asymptotic change-point analysis of the dependencies in time series Zeitreihenanalyse (DE-588)4067486-1 gnd Change-point-Problem (DE-588)4598971-0 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4598971-0 (DE-588)4113937-9 |
| title | Asymptotic change-point analysis of the dependencies in time series |
| title_auth | Asymptotic change-point analysis of the dependencies in time series |
| title_exact_search | Asymptotic change-point analysis of the dependencies in time series |
| title_full | Asymptotic change-point analysis of the dependencies in time series vorgelegt von Christoph Heuser |
| title_fullStr | Asymptotic change-point analysis of the dependencies in time series vorgelegt von Christoph Heuser |
| title_full_unstemmed | Asymptotic change-point analysis of the dependencies in time series vorgelegt von Christoph Heuser |
| title_short | Asymptotic change-point analysis of the dependencies in time series |
| title_sort | asymptotic change point analysis of the dependencies in time series |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd Change-point-Problem (DE-588)4598971-0 gnd |
| topic_facet | Zeitreihenanalyse Change-point-Problem Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029421435&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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