Analyzing and modeling multivariate association: statistical measures and pair-copula constructions
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Lohmar [u.a.]
Eul
2013
|
| Ausgabe: | 1. Aufl. |
| Schriftenreihe: | Reihe: Quantitative Ökonomie
176 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XXIV, 199 S. Ill., graph. Darst. |
| ISBN: | 9783844102291 |
Internformat
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| 245 | 1 | 0 | |a Analyzing and modeling multivariate association |b statistical measures and pair-copula constructions |c Julius Schnieders |
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| 264 | 1 | |a Lohmar [u.a.] |b Eul |c 2013 | |
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| 650 | 0 | 7 | |a Finanzmathematik |0 (DE-588)4017195-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kopula |g Mathematik |0 (DE-588)4529954-7 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804150315569643520 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
LIST OF FIGURES XI
LIST OF TABLES XVII
1. INTRODUCTION 1
2. COPULAS AND DEPENDENCE CONCEPTS 7
2.1. THEORY OF COPULAS 7
2.2. PARAMETRIC COPULA FAMILIES 12
2.2.1. BIVARIATE COPULA FAMILIES 12
2.2.2. MULTIVARIATE COPULA FAMILIES 15
2.3. SURVIVAL A N D ROTATED COPULAS 24
2.4. THE EMPIRICAL COPULA 27
2.5. MEASURES OF ASSOCIATION 28
2.5.1. PEARSON CORRELATION 28
2.5.2. CONCORDANCE 30
2.5.3. SPEARMAN S RHO 31
2.5.4. KENDALL S T A U 33
2.5.5. TAIL DEPENDENCE 34
3. ASSOCIATION O F RANDOM VECTORS 37
3.1. NOTATION A N D DEFINITIONS 38
HTTP://D-NB.INFO/1032088591
IMAGE 2
CONTENTS
3.2. ESTABLISHED MEASURES OF ASSOCIATION 39
3.2.1. CANONICAL CORRELATION 39
3.2.2. RV COEFFICIENT 40
3.2.3. DISTANCE CORRELATION 41
3.3. COPULA BASED MEASURES OF ASSOCIATION 42
3.3.1. M E A N OF PAIRWISE ASSOCIATION 4 3
3.3.2. PEARSON-LIKE COPULA MEASURES OF ASSOCIATION 45
3.3.3. SPEARMAN-LIKE COPULA MEASURES O F ASSOCIATION 51
3.4. STATISTICAL ESTIMATION OF THE MEASURES 53
3.5. EMPIRICAL EXAMPLE 6 3
3.6. INFLUENCE OF OUTLIERS 64
3.7. CONCLUSION 68
4. PAIR-COPULA CONSTRUCTIONS 71
4.1. PAIR-COPULA CONSTRUCTIONS 73
4.2. CONDITIONAL DISTRIBUTION FUNCTIONS 74
4.3. VINES 76
4.4. SIMPLIFIED PCCS 78
4.5. ESTIMATION OF PAIR-COPULA CONSTRUCTIONS 79
4.5.1. INFERENCE FUNCTIONS FOR MARGINS ESTIMATION 81
4.5.2. SEMIPARAMETRIC ESTIMATION 82
4.5.3. STEPWISE ESTIMATION 83
4.6. SIMULATION TECHNIQUES 84
4.7. CONCLUSION 86
5. MODEL SELECTION FOR PAIR-COPULA CONSTRUCTIONS 89
5.1. MODEL SELECTION FOR BIVARIATE COPULAS 91
5.1.1. INFORMATION CRITERIA 91
5.1.2. GRAPHICAL MODELS 92
5.2. GOODNESS-OF-FIT 95
5.3. MODEL SELECTION FOR VINE STRUCTURES 99
5.3.1. D-VINE STRUCTURES 103
5.3.2. CANONICAL VINE STRUCTURES 105
5.4. SIMULATION STUDY 105
5.4.1. ESTIMATION OF BIVARIATE COPULAS 107
5.4.2. D-VINE ALGORITHMS 108
5.4.3. CANONICAL VINE ALGORITHMS 109
5.5. APPLICATION TO EMPIRICAL DATASETS 110
5.5.1. STOCK RETURNS 110
5.5.2. EXCHANGE RATES 116
5.6. CONCLUSION 119
6. APPLICATION O F PAIR-COPULA CONSTRUCTIONS 121
6.1. DYNAMIC PCC MODELS: A N APPLICATION W I T H VALUE-AT-RISK
FORECASTING 121 6.1.1. COPULA-GARCH MODEL 123
IMAGE 3
CONTENTS IX
6.1.2. INFERENCE A N D SIMULATION 125
6.1.3. ALTERNATIVE/BENCHMARK MODELS 127
6.1.4. BACKTESTING METHODS 128
6.1.5. EMPIRICAL RESULTS 131
6.1.6. CONCLUSION 138
6.2. SPATIAL DEPENDENCE IN W I N D A N D OPTIMAL W I N D P O W E R
ALLOCATION . . . 139 6.2.1. DATA A N D W I N D S P E E D MODELS 143
6.2.2. OPTIMAL W I N D POWER ALLOCATION 152
6.2.3. CONCLUSION 157
A. MEASURES OF ASSOCIATION: ADDITIONAL TABLES 159
B. PCC ESTIMATORS: ADDITIONAL TABLES 177
C. COPULA-GARCH MODELS: ADDITIONAL TABLES 183
D. SPATIAL DEPENDENCE IN WIND POWER: ADDITIONAL TABLES 187
BIBLIOGRAPHY 191
Many applications in quantitative finance, such as the estimation of the Value-at-Risk of a portfo¬
lio, require the modeling of dependencies of a large number of random variables. The most popu¬
lar approach is Pearson s correlation coefficient, which is based on the covariance, i. e. the mixed
second moments of the corresponding random variables. However, the correlation coefficient
only captures linear dependencies and solely in case of a few distributions, such as the multivari-
ate normal distribution, completely determines the dependence structure.
Empirical data, unfortunately, is often non-normal and exhibits asymmetric dependence patterns.
The multivariate normal distribution, for example, often underestimates the probability of simul¬
taneous extremes, which can lead to incorrect estimates of the risk of a given portfolio. Hence,
for many empirical applications, the normal distribution is not suitable.
As an alternative concept of dependence modeling, the theory of copulas has drawn a lot of at¬
tention in the past decades. Based on this theory, the author introduces a new class of measures
of association between random vectors that are invariant with respect to the marginal distribu¬
tion functions of the considered random vectors and can distinguish between positive and nega¬
tive association.
The second part of the thesis focuses on the modeling of high dimensional dependencies with
Pair-copula constructions. To this end, a data-driven sequential estimation method for these
models is developed. Empirical applications of these models in Value-at-Risk forecasting and the
spatial modeling of meteorological data are given.
|
| any_adam_object | 1 |
| author | Schnieders, Julius 1983- |
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| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.01519535 |
| dewey-search | 332.01519535 |
| dewey-sort | 3332.01519535 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| edition | 1. Aufl. |
| format | Thesis Book |
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| id | DE-604.BV040992258 |
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| indexdate | 2024-07-10T00:36:58Z |
| institution | BVB |
| isbn | 9783844102291 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025970032 |
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| series | Reihe: Quantitative Ökonomie |
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| spelling | Schnieders, Julius 1983- Verfasser (DE-588)1033630152 aut Analyzing and modeling multivariate association statistical measures and pair-copula constructions Julius Schnieders 1. Aufl. Lohmar [u.a.] Eul 2013 XXIV, 199 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Reihe: Quantitative Ökonomie 176 Zugl.: Köln, Univ., Diss., 2012 Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Ökonometrie (DE-588)4132280-0 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Kopula Mathematik (DE-588)4529954-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Finanzmathematik (DE-588)4017195-4 s Ökonometrie (DE-588)4132280-0 s Multivariate Analyse (DE-588)4040708-1 s Kopula Mathematik (DE-588)4529954-7 s DE-604 Reihe: Quantitative Ökonomie 176 (DE-604)BV023548254 176 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025970032&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025970032&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Schnieders, Julius 1983- Analyzing and modeling multivariate association statistical measures and pair-copula constructions Reihe: Quantitative Ökonomie Multivariate Analyse (DE-588)4040708-1 gnd Ökonometrie (DE-588)4132280-0 gnd Finanzmathematik (DE-588)4017195-4 gnd Kopula Mathematik (DE-588)4529954-7 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4132280-0 (DE-588)4017195-4 (DE-588)4529954-7 (DE-588)4113937-9 |
| title | Analyzing and modeling multivariate association statistical measures and pair-copula constructions |
| title_auth | Analyzing and modeling multivariate association statistical measures and pair-copula constructions |
| title_exact_search | Analyzing and modeling multivariate association statistical measures and pair-copula constructions |
| title_full | Analyzing and modeling multivariate association statistical measures and pair-copula constructions Julius Schnieders |
| title_fullStr | Analyzing and modeling multivariate association statistical measures and pair-copula constructions Julius Schnieders |
| title_full_unstemmed | Analyzing and modeling multivariate association statistical measures and pair-copula constructions Julius Schnieders |
| title_short | Analyzing and modeling multivariate association |
| title_sort | analyzing and modeling multivariate association statistical measures and pair copula constructions |
| title_sub | statistical measures and pair-copula constructions |
| topic | Multivariate Analyse (DE-588)4040708-1 gnd Ökonometrie (DE-588)4132280-0 gnd Finanzmathematik (DE-588)4017195-4 gnd Kopula Mathematik (DE-588)4529954-7 gnd |
| topic_facet | Multivariate Analyse Ökonometrie Finanzmathematik Kopula Mathematik Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025970032&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025970032&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023548254 |
| work_keys_str_mv | AT schniedersjulius analyzingandmodelingmultivariateassociationstatisticalmeasuresandpaircopulaconstructions |