α-stable random vectors with time varying spectral measure and applications to financial time series analysis:
Gespeichert in:
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
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Berlin
Pro Business
2008
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| Ausgabe: | 1. Aufl. |
| Schriftenreihe: | Quantitative Wirtschaftsforschung
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 351 S. graph. Darst. |
| ISBN: | 9783868050844 |
Internformat
MARC
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| 100 | 1 | |a Hartz, Christoph |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a α-stable random vectors with time varying spectral measure and applications to financial time series analysis |c Christoph Hartz |
| 246 | 1 | |a [Alpha]-stable random vectors with time varying spectral measure and applications to financial time series analysis | |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a Berlin |b Pro Business |c 2008 | |
| 300 | |a XIV, 351 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Quantitative Wirtschaftsforschung | |
| 502 | |a Zugl.: München, Univ., Diss., 2008 | ||
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| 650 | 0 | 7 | |a Aktienrendite |0 (DE-588)4126593-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zufallsvektor |0 (DE-588)4191098-9 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Zufallsvektor |0 (DE-588)4191098-9 |D s |
| 689 | 0 | 2 | |a Zeitreihenanalyse |0 (DE-588)4067486-1 |D s |
| 689 | 0 | |5 DE-604 | |
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Datensatz im Suchindex
| _version_ | 1804137512790130688 |
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| adam_text | Contents
List of Tables vii
List of Figures xi
1 Introduction 1
2 Stable Random Vectors 5
2.1 Definitions.................................... 5
2.2 Univariate Stable Random Variables ..................... 8
2.2.1 Definitions................................ 8
2.2.2 Properties................................ 12
2.3 Properties.................................... 20
2.4 Dependency Measures ............................. 25
2.4.1 Codifference............................... 25
2.4.2 Covariation............................... 2(i
2.5 Sub Gaussian Stable Random Vectors .................... 30
3 Event Studies for Conditionally Varying Stable Random Variables 37
3.1 Introduction................................... 37
3.2 Market Efficiency and Event Studios ..................... 38
3.3 Event Studies in the. Presence, of Conditional Heteroscedastieity and Heavy
Tails....................................... 39
3.3.1 Normal Returns............................. 39
3.3.2 Abnormal Returns..................,........ 42
3.3.3 Cumulative Abnormal Returns .................... 42
3.3.4 Alternative Test, Statistics....................... 43
3.4 Filing for Insolvency: An Event Study for the German Neuer Markt . . 45
3.4.1 Filing for Insolvency.......................... 46
3.4.2 Empirical Results............................ 47
3.5 Summary .................................... 59
iv_____________________________________________________Table of Contents
4 Factor Models for Stable Random Vectors with Time Varying Spec-
tral Measure 61
4.1 Introduction................................... Gl
4.2 Factor Models for Stable Random Vectors .................. G4
4.2.1 Symmetric Fat-tor Models for Stable Random Vectors........ 09
4.2.2 Stable Factor-GARCH Models .................... 73
4.3 Portfolio Optimization for Gorman DAX Stocks Using a Stable Factor
GARCH Model................................. 74
4.3.1 Portfolio Selection and Risk Assessment ...............75
4.3.2 Empirical Results............................ 77
4.4 Summary .................................... 89
5 Simulated Likelihood Estimation of Sub-Gaussian Stable Densities 93
5.1 Introduction................................... 93
5.2 Empirical Estimators for the Spectral Measure of Sub -Gaussian Stable
Random Vectors ................................ 97
5.2.1 The Empirical Estimator........................ 98
5.2.2 The Modified Empirical Estimator ..................100
5.2.3 Monte Carlo Performance.......................102
5.3 Simulated Density Calculation for Sub Gaussian Stable Random Vectors . 10G
5.3.1 Consistency of Simulated Density................... 110
5.3.2 Simulated Likelihood Calculation for Sub-Gaussian Stable Random
Vet-tors.................................. Ill
5.3.3 Modified Random Number Generation................ 113
5.4 Monte Carlo Results.............................. 114
5.4.1 Simulated Density Calculation for Univariate Symmetric Stable Ran-
dom Variables..............................114
5.4.2 Simulated Likelihood Estimation for Univariate Symmetric Stable
Random Variables ...........................125
5.4.3 Simulated Likelihood Estimation for Sub Gaussian Stable Random
Vectors..................................129
5.5 Summary ....................................134
6 Conditional Covariation Models for Sub-Gaussian Stable Random
Vectors 137
G.I Introduction...................................137
G.2 Conditional Sub Gaussian Stable Random Vectors..............140
6.3 Conditional Covariation Models for Sub-Gaussian Stable Random Vectors 143
6.3.1 General Structure............................144
Table of Contents
6.3.2 The Constant Conditional Covariation Model ............148
0.3.3 The Dynamic Conditional Covariation Model ............158
0.4 Portfolio Optimization Using Conditional Covariation Models .......106
0.4.1 The Datasets..............................109
0.4.2 Empirical Results............................176
0.5 Summary ....................................193
7 Conclusions 197
Appendices
A Mathematical Appendix 201
B Empirical Estimators for the Spectral Measure of Sub-Gaussian
Stable Random Vectors — Monte Carlo Results 203
C Simulated Density Calculation for Univariate Symmetric Stable
Random Variables — Monte Carlo Results 221
C.I Random Number Set...............................222
C.2 Halton Number Set...............................228
D Simulated Likelihood Estimation for Univariate Symmetric Stable
Random Variables — Monte Carlo Results 235
E Simulated Likelihood Estimation for Sub-Gaussian Stable Random
Vectors — Monte Carlo Results 253
F Constant Condition Covariation Estimators — Monte Carlo Re-
sults 271
G Portfolio Optimization Using Conditional Covariation Models —
Empirical Results 285
G.I Germany Dataset................................285
G.I.I Univariate Estimation Results.....................285
G.1.2 Multivariate Estimation Results....................287
G.1.3 Portfolio Results ............................288
G.2 World Dataset..................................293
G.2.1 Univariate Estimation Results.....................293
G.2.2 Multivariate Estimation Results....................29C
G.2.3 Portfolio Results............................300
G.3 Dow Jones Datasets...............................307
Table of Contents
G.4 First Dow Jones Dataset............................ 308
G.4.1 Univariate Estimation Results..................... 308
G.4.2 Multivariate Estimation Results.................... 315
G.4.3 Portfolio Results ............................ 319
G.5 Second Dow Jones Dataset........................... 325
G.5.1 Univariate Estimation Results..................... 325
G.5.2 Multivariate Estimation Results.................... 331
G.5.3 Portfolio Results ............................ 334
Bibliography 341
List of Tables
3.1 Announcement Dates and Event Dnt.es...................... 47
3.2 Estimation Period Test Statistics......................... 49
3.3 Estimation Period Test Statistics (cont)..................... 50
3.4 Market Model Comparison ............................ 51
3.5 Estimation Results for Market Model with Individual Shape Parameter .... 53
3.0 Estimation Results for Market Model with Common Shape Parameter .... 54
3.7 Event Period Test Statistics Comparison..................... 57
4.1 Summary Statistics for Asset and Index Returns Series............. 77
4.2 Estimation Results for the Stable factor GARCH Models ........... 79
4.3 Value at Risk Coverage. MRP. No Short Selling................ 84
4.4 Value at Risk Coverage. MRP. Short. Selling Allowed ............. 80
4.5 Value at Risk Coverage-. EWP.......................... 88
0.1 Summary Statistics for the Germany DatasetReturn Series.......... 170
0.2 Summary Statistics for the World Dataset Return Series............ 173
0.3 Summary Statistics for the First Dow Jones Dataset Return Series...... 174
0.4 Summary Statistics for the Second Dow Jones Dataset Return Scries..... 175
0.5 Univariate Estimation Results. Germany. AR(1). free 3............. 170
0.0 Conditional Covariation Estimation Results. Germany. AR(1)......... 177
0.7 VaR Coverage. MRP. Germany. AR(1). Dynamic Conditional Covariation . . 180
0.8 VaR Coverage. EWP. Germany. AR(1). Dynamic Conditional Covariation . . 182
O. J Conditional Covariation Estimation Results. World. AR(1)........... 185
0.10 VaR Coverage. MRP. World. AR(1). Dynamic Conditional Covariation .... 187
0.11 Model Comparison................................. 1(J3
B.I BIAS for both Empirical Estimators. p = -0.9 ................. 205
B.2 MSE for both Empirical Estimators, p = -0.9.................. 207
B.3 BIAS for both Empirical Estimators, p - -0.5 ................. 209
B.4 MSE for both Empirical Estimators, p = -0.5.................. 211
B.5 BIAS for both Empirical Estimators, p = -0.1 ................. 213
List of Tables
B.6 MSE for both Empirical Estimators, p = -0.1..................215
B.7 BIAS for both Empirical Estimators, p = 0.0..................217
B.8 MSE for both Empirical Estimators, p = 0.0...................219
C.I Descriptive Statistics for MADR. Random Number Set.............222
C.2 Descriptive Statistics for MARDR. Random Number Set............223
C.3 Descriptive Statistics for OBR. Random Number Set..............224
C.4 Descriptive Statistics for ORBr. Random Number Set.............225
C.5 Descriptive Statistics for OADR. Random Number Set.............220
C.C Descriptive Statistics for ORDR. Random Number Set.............227
C.7 Descriptive Statistics for MADR, Halton Number Set..............228
C.8 Descriptive Statistics for MARDR. Halton Number Set.............229
C.9 Descriptive Statistics for OBB. Halton Number Set...............230
CIO Descriptive Statistics for ORBj?, Halton Number Set..............231
C.ll Descriptive Statistics for OADjj, Halton Number Set..............232
C.12 Descriptive Statistics for ORDfi, Halton Number Set..............233
D.I Univariate Simulated Likelihood Estimator, a = 1.9, fixed R..........236
D.2 Univariate Simulated Likelihood Estimator, a = 1.9, relative R........237
D.3 Univariate Simulated Likelihood Estimator, a = 1.8, fixed R..........238
D.4 Univariate Simulated Likelihood Estimator, a = 1.8, relative R........239
D.5 Univariate Simulated Likelihood Estimator, a = 1.7, fixed R..........240
D.6 Univariate Simulated Likelihood Estimator, a = 1.7, relative R........241
D.7 Univariate Simulated Likelihood Estimator, a = 1.6. fixed R..........242
D.8 Univariate Simulated Likelihood Estimator, a = 1.6. relative R........243
D.9 Univariate Simulated Likelihood Estimator, a = 1.5. fixed R..........244
D.K) Univariate Simulated Likelihood Estimator, a = 1.5. relative R........245
D.ll Univariate Simulated Likelihood Estimator, a = 1.4. fixed R..........240
D.12 Univariate Simulated Likelihood Estimator, a = 1.4. relative R........247
D.13 Univariate Simulated Likelihood Estimator, a = 1.3. fixed R..........248
D.14 Univariate Simulated Likelihood Estimator, a = 1.3. relative R........249
D.15 Univariate Simulated Likelihood Estimator, a = 1.2. fixed R..........250
D.10 Univariate Simulated Likelihood Estimator, a = 1.2. relative R........251
E.I BIAS for the Multivariate Simulated Likelihood Estimator, p = -0.9..... 254
E.2 BIAS for the Multivariate Simulated Likelihood Estimator, p = -0.9 (cont) . 255
E.3 MSE for the Multivariate Simulated Likelihood Estimator, p = —0.9..... 256
E.4 MSE for the Multivariate Simulated Likelihood Estimator, p = -0.9 (cont) . . 257
E.5 BIAS for the Multivariate Simulated Likelihood Estimator, p = -0.5..... 258
E.O BIAS for the Multivariate Simulated Likelihood Estimator, p = -0.5 (cont) . 259
List of Tables
E.7 MSE for the Multivariate Simulated Likelihood Estimator, p = —0.5 .....200
E.8 MSE for the Multivariate Simulated Likelihood Estimator, p = -0.9 (cont) . . 2G1
E.U BIAS for the Multivariate Simulated Likelihood Estimator, p = -0.1.....202
E.10 BIAS for the Multivariate Simulated Likelihood Estimator, p = -0.1 (cont) . 203
E.ll MSE for the Multivariate Simulated Likelihood Estimator, p = -0.1 .....2G4
E.12 MSE for the Multivariate Simulated Likelihood Estimator, p = -0.1 (cont) . . 265
E.13 BIAS for the Multivariate Simulated Likelihood Estimator, p = 0.0......200
E.14 BIAS for the Multivariate Simulated Likelihood Estimator, p = 0.0 (cont) . . 207
E.15 MSE for the Multivariate Simulated Likelihood Estimator, p = 0.0 ......208
E.10 MSE for the Multivariate Simulated Likelihood Estimator, p = 0.0 (cont) . . . 209
F.I BIAS for the Constant Condition Covariation Estimators. R12 = -1.00 .... 272
F.2 MSE for the Constant Condition Covariation Estimators. Ri2 = —1.00 .... 273
F.3 BIAS for the Constant Condition Covariation Estimators. Rl2 = -0.50 .... 274
F.4 MSE for the Constant Condition Covariation Estimators. Ri2 = -0.50 .... 275
F.5 BIAS for the Constant Condition Covariation Estimators. Ri2 = 0.25.....270
F.O MSE for the Constant Condition Covariation Estimators. Rl2 = 0.25.....277
F.7 BIAS for the Constant Condition Covariation Estimators. Ri2 = 0.50.....278
F.8 MSE for the Constant Condition Covariation Estimators. Rn = 0.50.....279
F.9 BIAS for the Constant Condition Covariation Estimators. Rn = 1.00.....280
F.10 MSE for the Constant Condition Covariation Estimators. Ru = 1.00.....281
F.ll BIAS for the Constant Condition Covariation Estimators. Ru = 1.50.....282
F.12 MSE for the Constant Condition Covariation Estimators. Ri2 = 1.50.....283
G.I Univariate Estimation Results. Germany. AR(1). ,3 = 0.............280
G.2 Univariate Estimation Results. Germany. AR(0). free 3.............280
G.3 Univariate Estimation Results. Germany. AR(0). 3 = 0.............280
G.4 Conditional Covariation Estimation Results. Germany. AR(0).........287
G.5 VaR Coverage. MRP. Germany. AR(1). Constant Conditional Covariation . . 288
G.O VaR Coverage. MRP. Germany. AR(0). Constant Conditional Covariation . . 289
G.7 VaR Coverage. MRP. Germany. AR(0). Dynamic Conditional Covariation . . 289
G.8 VaR Coverage. EWP. Germany. AR(1). Constant Conditional Covariation . . 290
G.9 VaR Coverage. EWP. Germany. AR(0). Constant, Conditional Covariation . . 291
G.10 VaR Coverage. EWP, Germany. AR(0). Dynamic Conditional Covariation . . 291
G.ll Univariate Estimation Results, World, AR(1). free 3..............293
G.12 Univariate Estimation Results, World. AR(1). /3 = 0..............294
G.13 Univariate Estimation Results, World, AR(0). free 0..............294
G.14 Univariate Estimation Results, World. AR(0). f3 = 0..............295
G.15 Conditional Covariation Estimation Results. World, AR(0)...........297
List of Tables
G.16 VaR Coverage. MRP. World, AR(1). Constant Conditional Covariation .... 301
G.17 VaR Coverage. MRP. World. AR(0). Constant Conditional Covariation .... 301
G.18 VaR Coverage. MRP. World. AR(0). Dynamic Conditional Covariation .... 303
G.19 VaR Coverage, EWP, World, AR(1). Constant Conditional Covariation .... 304
G.20 VaR Coverage. EWP, World, AR(1). Dynamic Conditional Covariation .... 304
G.21 VaR Coverage, EWP. World. AR(0). Constant Conditional Covariation .... 305
G.22 VaR Coverage, EWP, World. AR(0). Dynamic Conditional Covariation .... 305
G.23 The Dow Jones Stocks...............................307
G.24 Univariate Estimation Results, First Dow Jones, AR(1). free j3 ........308
G.25 Univariate Estimation Results, First Dow Jones. AR(1). /? = 0.........309
G.26 Univariate Estimation Results, First Dow Jones, AR(0), free (3 ........311
G.27 Univariate Estimation Results, First Dow Jones, AR(0), /? = 0.........313
G.28 Conditional Covariation Estimation Results, First Dow Jones, AR(1).....315
G.29 Conditional Covariation Estimation Results, First Dow Jones, AR(0).....316
G.30 VaR Coverage, MRP, First DJ, AR(1), Constant Conditional Covariation . . . 319
G.31 VaR Coverage, MRP, First DJ, AR(1). Dynamic Conditional Covariation ... 319
G.32 VaR Coverage, MRP, First DJ, AR(0). Constant Conditional Covariation ... 320
G.33 VaR Coverage, MRP, First DJ, AR(0), Dynamic Conditional Covariation ... 321
G.34 VaR Coverage, EWP, First DJ, AR(1). Constant Conditional Covariation . . 322
G.35 VaR Coverage, EWP. First DJ, AR(1). Dynamic Conditional Covariation ... 322
G.36 VaR Coverage. EWP. First DJ. AR(0), Constant Conditional Covariation . . 323
G.37 VaR Coverage. EWP. First DJ, AR(0), Dynamic Conditional Covariation ... 323
G.38 Univariate Estimation Results. Second Dow Jones, AR(1), free /3.......325
G.39 Univariate Estimation Results. Second Dow Jones, AR(1). 0 = 0.......326
G.40 Univariate Estimation Results, Second Dow Jones, AR(0). free j3.......327
G.41 Univariate Estimation Results. Second Dow Jones. AR(0). (5 - 0.......329
G.42 Conditional Covariation Estimation Results. Second Dow Jones. AR(1) .... 331
G.43 Conditional Covariation Estimation Results. Second Dow Jones. AR(0) .... 332
G.44 VaR Coverage. MRP. Second DJ. AR(1). Constant Conditional Covariation . 334
G.45 VaR Coverage. MRP. Second DJ, AR(1). Dynamic Conditional Covariation . 334
G.46 VaR Coverage. MRP. Second DJ. AR(0). Constant Conditional Covariation . 335
G.47 VaR Coverage. MRP. Second DJ. AR(0). Dynamic Conditional Covariation . 33G
G.48 VaR Coverage. EWP. Second DJ. AR(1), Constant Conditional Covariation . 337
G.49 VaR Coverage. EWP. Second DJ. AR(1). Dynamic Conditional Covariation . 337
G.50 VaR Coverage. EWP, Second D.I. AR(0). Constant Conditional Covariation . 338
G.51 VaR Coverage. EWP, Second DJ, AR(0). Dynamic Conditional Covariation . 338
List of Figures
2.1 Discontinuity for q = 1 and j/0 ........................ 9
2.2 Shape and Tail Behavior of Symmetric o stable Density Functions...... 13
2.3 Shape of Asymmetric and Totally Right Skewed a stable Density Functions . 1G
2.4 Multivariate Density Functions Gaussian vs. Sub Gaussian......... 33
2.5 Multivariate Density Contours Gaussian vs. Sub Gaussian......... 34
3.1 Event Period Test Statistics............................ 5G
4.1 Asset, and Index Return Seri « .......................... 78
4.2 Estimated Factor Scales.............................. 80
4.3 Portfolio Weights. MRP. No Short Selling.................... 81
4.4 Portfolio Weights. MRP. Short Selling Allowed................. 82
4.5 Empirical Downfall Probability Distribution. MRP. No Short Selling..... 85
4.G Empirical Downfall Probability Distribution. MRP. Short Selling Allowed . . 87
4.7 Empirical Downfall Probability Distribution. EWP............... 89
4.8 Transaction Cost Equivalents. MRP. No Short Selling............. 90
4.9 Transaction Cost Equivalents. MRP. Short Selling Allowed .......... 91
5.1 BIAS for the Modified Empirical Estimator................... 103
5.2 MSE for the Modified Empirical Estimator ................... 104
5.3 MSE of p for the Modified Empirical Estimator ................ 105
5.4 Empirical Distribution and Descriptive Statistics for MADb.......... 11G
5.5 Empirical Distribution and Descriptive Statistics for MARDr......... 118
5.G Empirical Distribution and Descriptive Statistics for OBfi........... 120
5.7 Empirical Distribution and Descriptive Statistics for ORBH.......... 121
5.8 Empirical Distribution and Descriptive Statistics for OAD/(.......... 123
5.9 Empirical Distribution and Descriptive Statistics for ORDfl.......... 124
5.10 BIAS for the Univariate Simulated Likelihood Estimator............ 127
5.11 Relative Efficiency for the Univariate Simulated Likelihood Estimator..... 128
5.12 BIAS for the Multivariate Simulated Likelihood Estimator........... 131
5.13 MSE for the Multivariate Simulated Likelihood Estimator........... 132
List of Figures
5.14 MSE of p for the Mmtivariate Simulated Likelihood Estimator.........133
6.1 Constant Conditional Covariation Estimators Comparison. BIAS.......156
6.2 Constant Conditional Covariation Estimators Comparison. MSE........157
6.3 Germany Dataset Index and Return Series....................170
6.4 World Dataset Index and Return Series.....................172
6.5 £( and Components, Germany. AR(1)......................178
6.6 Portfolio Weights. MRP. Germany. AR(1)....................179
6.7 Empirical Downfall Probabilities, MRP, Germany, AR(1), Dynamic Models . 181
6.8 Empirical Downfall Probabilities, EWP. Germany. AR(1). Dynamic Models . 183
6.9 Components of E,. World, AR(1).........................186
6.10 Empirical Downfall Probabilities, MRP, World, AR(1), Dynamic Models ... 188
B.I BIAS for the Modified Empirical Estimator, p = -0.9 .............204
B.2 MSE for the Modified Empirical Estimator, p = -0.9..............206
B.3 BIAS for the Modified Empirical Estimator, p = -0.5 .............208
B.4 MSE for the Modified Empirical Estimator, p = -0.5..............210
B.5 BIAS for the Modified Empirical Estimator, p = -0.1 .............212
B.6 MSE for the Modified Empirical Estimator, p = -0.1..............214
B.7 BIAS for the Modified Empirical Estimator, p = 0.0 ..............216
B.8 MSE for the Modified Empirical Estimator, p = 0.0...............218
G.I Parameter Restrictions, Germany, AR(1).....................285
G.2 Parameter Restrictions, Germany, AR(0).....................286
G.3 £( and Components. Germany. AR(0)......................287
G.4 Portfolio Weights. MRP. Germany. AR(0)....................288
G.5 Empirical Downfall Probabilities. MRP. Germany. AR(0), Dynamic Models . 290
G.6 Empirical Downfall Probabilities. EWP. Germany. AR(0). Dynamic Models . 292
G.7 Parameter Restrictions. World. AR(1)......................293
G.8 Parameter Restrictions. World. AR(0)......................295
G.9 £(. World. AR(1) .................................296
G.10 Et. World. AR(0) .................................298
G.ll Components of £,. World. AR(0).........................299
G.12 Portfolio Weights. MRP. World. AR(1)......................300
G.13 Portfolio Weights. MRP. World. AR(0)......................302
G.14 Empirical Downfall Probabilities, MRP, World. AR(0). Dynamic Models ... 303
G.15 Empirical Downfall Probabilities. EWP. World, AR(1), Dynamic Models ... 306
G.1C Empirical Downfall Probabilities. EWP. World. AR(0). Dynamic Models ... 306
G.I7 Parameter Restrictions, First Dow Jones, AR(1) ................309
G.18 Parameter Restrictions, First Dow Jones, AR(0) ................312
List of Figures
G.l J Empirical Downfall Probabilities. MRP. First D.I. AR(1). Dynamic Models . . 320
G.20 Empirical Downfall Probabilities. MRP. First D.I. AR(0). Dynamic Models . . 321
G.21 Empirical Downfall Probabilities. EWP. First D.I. AR(1). Dynamic Models . . 324
G.22 Empirical Downfall Probabilities. EWP. First D.I. AR(0). Dynamic Models . . 324
G.23 Parameter Restrictions. Second Dow Jones. AR(1) ...............32(i
G.24 Parameter Restrictions. Second Dow Jones. AR(0) ...............328
G.25 Empirical Downfall Probabilities. MRP. Second D.I. AR(1). Dynamic Models 335
G.20 Empirical Downfall Probabilities. MRP. Second D.I. AR(0). Dynamic Models 330
G.27 Empirical Downfall Probabilities. EWP. Second D.I. AR(1). Dynamic Models 339
G.28 Empirical Downfall Probabilities. EWP. Second D.I. AR(0). Dynamic Models 339
|
| adam_txt |
Contents
List of Tables vii
List of Figures xi
1 Introduction 1
2 Stable Random Vectors 5
2.1 Definitions. 5
2.2 Univariate Stable Random Variables . 8
2.2.1 Definitions. 8
2.2.2 Properties. 12
2.3 Properties. 20
2.4 Dependency Measures . 25
2.4.1 Codifference. 25
2.4.2 Covariation. 2(i
2.5 Sub Gaussian Stable Random Vectors . 30
3 Event Studies for Conditionally Varying Stable Random Variables 37
3.1 Introduction. 37
3.2 Market Efficiency and Event Studios . 38
3.3 Event Studies in the. Presence, of Conditional Heteroscedastieity and Heavy
Tails. 39
3.3.1 Normal Returns. 39
3.3.2 Abnormal Returns.,. 42
3.3.3 Cumulative Abnormal Returns . 42
3.3.4 Alternative Test, Statistics. 43
3.4 Filing for Insolvency: An Event Study for the German Neuer Markt . . 45
3.4.1 Filing for Insolvency. 46
3.4.2 Empirical Results. 47
3.5 Summary . 59
iv_Table of Contents
4 Factor Models for Stable Random Vectors with Time Varying Spec-
tral Measure 61
4.1 Introduction. Gl
4.2 Factor Models for Stable Random Vectors . G4
4.2.1 Symmetric Fat-tor Models for Stable Random Vectors. 09
4.2.2 Stable Factor-GARCH Models . 73
4.3 Portfolio Optimization for Gorman DAX Stocks Using a Stable Factor
GARCH Model. 74
4.3.1 Portfolio Selection and Risk Assessment .75
4.3.2 Empirical Results. 77
4.4 Summary . 89
5 Simulated Likelihood Estimation of Sub-Gaussian Stable Densities 93
5.1 Introduction. 93
5.2 Empirical Estimators for the Spectral Measure of Sub -Gaussian Stable
Random Vectors . 97
5.2.1 The Empirical Estimator. 98
5.2.2 The Modified Empirical Estimator .100
5.2.3 Monte Carlo Performance.102
5.3 Simulated Density Calculation for Sub Gaussian Stable Random Vectors . 10G
5.3.1 Consistency of Simulated Density. 110
5.3.2 Simulated Likelihood Calculation for Sub-Gaussian Stable Random
Vet-tors. Ill
5.3.3 Modified Random Number Generation. 113
5.4 Monte Carlo Results. 114
5.4.1 Simulated Density Calculation for Univariate Symmetric Stable Ran-
dom Variables.114
5.4.2 Simulated Likelihood Estimation for Univariate Symmetric Stable
Random Variables .125
5.4.3 Simulated Likelihood Estimation for Sub Gaussian Stable Random
Vectors.129
5.5 Summary .134
6 Conditional Covariation Models for Sub-Gaussian Stable Random
Vectors 137
G.I Introduction.137
G.2 Conditional Sub Gaussian Stable Random Vectors.140
6.3 Conditional Covariation Models for Sub-Gaussian Stable Random Vectors 143
6.3.1 General Structure.144
Table of Contents
6.3.2 The Constant Conditional Covariation Model .148
0.3.3 The Dynamic Conditional Covariation Model .158
0.4 Portfolio Optimization Using Conditional Covariation Models .106
0.4.1 The Datasets.109
0.4.2 Empirical Results.176
0.5 Summary .193
7 Conclusions 197
Appendices
A Mathematical Appendix 201
B Empirical Estimators for the Spectral Measure of Sub-Gaussian
Stable Random Vectors — Monte Carlo Results 203
C Simulated Density Calculation for Univariate Symmetric Stable
Random Variables — Monte Carlo Results 221
C.I Random Number Set.222
C.2 Halton Number Set.228
D Simulated Likelihood Estimation for Univariate Symmetric Stable
Random Variables — Monte Carlo Results 235
E Simulated Likelihood Estimation for Sub-Gaussian Stable Random
Vectors — Monte Carlo Results 253
F Constant Condition Covariation Estimators — Monte Carlo Re-
sults 271
G Portfolio Optimization Using Conditional Covariation Models —
Empirical Results 285
G.I Germany Dataset.285
G.I.I Univariate Estimation Results.285
G.1.2 Multivariate Estimation Results.287
G.1.3 Portfolio Results .288
G.2 World Dataset.293
G.2.1 Univariate Estimation Results.293
G.2.2 Multivariate Estimation Results.29C
G.2.3 Portfolio Results.300
G.3 Dow Jones Datasets.307
Table of Contents
G.4 First Dow Jones Dataset. 308
G.4.1 Univariate Estimation Results. 308
G.4.2 Multivariate Estimation Results. 315
G.4.3 Portfolio Results . 319
G.5 Second Dow Jones Dataset. 325
G.5.1 Univariate Estimation Results. 325
G.5.2 Multivariate Estimation Results. 331
G.5.3 Portfolio Results . 334
Bibliography 341
List of Tables
3.1 Announcement Dates and Event Dnt.es. 47
3.2 Estimation Period Test Statistics. 49
3.3 Estimation Period Test Statistics (cont). 50
3.4 Market Model Comparison . 51
3.5 Estimation Results for Market Model with Individual Shape Parameter . 53
3.0 Estimation Results for Market Model with Common Shape Parameter . 54
3.7 Event Period Test Statistics Comparison. 57
4.1 Summary Statistics for Asset and Index Returns Series. 77
4.2 Estimation Results for the Stable factor GARCH Models . 79
4.3 Value at Risk Coverage. MRP. No Short Selling. 84
4.4 Value at Risk Coverage. MRP. Short. Selling Allowed . 80
4.5 Value at Risk Coverage-. EWP. 88
0.1 Summary Statistics for the Germany DatasetReturn Series. 170
0.2 Summary Statistics for the World Dataset Return Series. 173
0.3 Summary Statistics for the First Dow Jones Dataset Return Series. 174
0.4 Summary Statistics for the Second Dow Jones Dataset Return Scries. 175
0.5 Univariate Estimation Results. Germany. AR(1). free 3. 170
0.0 Conditional Covariation Estimation Results. Germany. AR(1). 177
0.7 VaR Coverage. MRP. Germany. AR(1). Dynamic Conditional Covariation . . 180
0.8 VaR Coverage. EWP. Germany. AR(1). Dynamic Conditional Covariation . . 182
O.'J Conditional Covariation Estimation Results. World. AR(1). 185
0.10 VaR Coverage. MRP. World. AR(1). Dynamic Conditional Covariation . 187
0.11 Model Comparison. 1(J3
B.I BIAS for both Empirical Estimators. p = -0.9 . 205
B.2 MSE for both Empirical Estimators, p = -0.9. 207
B.3 BIAS for both Empirical Estimators, p - -0.5 . 209
B.4 MSE for both Empirical Estimators, p = -0.5. 211
B.5 BIAS for both Empirical Estimators, p = -0.1 . 213
List of Tables
B.6 MSE for both Empirical Estimators, p = -0.1.215
B.7 BIAS for both Empirical Estimators, p = 0.0.217
B.8 MSE for both Empirical Estimators, p = 0.0.219
C.I Descriptive Statistics for MADR. Random Number Set.222
C.2 Descriptive Statistics for MARDR. Random Number Set.223
C.3 Descriptive Statistics for OBR. Random Number Set.224
C.4 Descriptive Statistics for ORBr. Random Number Set.225
C.5 Descriptive Statistics for OADR. Random Number Set.220
C.C Descriptive Statistics for ORDR. Random Number Set.227
C.7 Descriptive Statistics for MADR, Halton Number Set.228
C.8 Descriptive Statistics for MARDR. Halton Number Set.229
C.9 Descriptive Statistics for OBB. Halton Number Set.230
CIO Descriptive Statistics for ORBj?, Halton Number Set.231
C.ll Descriptive Statistics for OADjj, Halton Number Set.232
C.12 Descriptive Statistics for ORDfi, Halton Number Set.233
D.I Univariate Simulated Likelihood Estimator, a = 1.9, fixed R.236
D.2 Univariate Simulated Likelihood Estimator, a = 1.9, relative R.237
D.3 Univariate Simulated Likelihood Estimator, a = 1.8, fixed R.238
D.4 Univariate Simulated Likelihood Estimator, a = 1.8, relative R.239
D.5 Univariate Simulated Likelihood Estimator, a = 1.7, fixed R.240
D.6 Univariate Simulated Likelihood Estimator, a = 1.7, relative R.241
D.7 Univariate Simulated Likelihood Estimator, a = 1.6. fixed R.242
D.8 Univariate Simulated Likelihood Estimator, a = 1.6. relative R.243
D.9 Univariate Simulated Likelihood Estimator, a = 1.5. fixed R.244
D.K) Univariate Simulated Likelihood Estimator, a = 1.5. relative R.245
D.ll Univariate Simulated Likelihood Estimator, a = 1.4. fixed R.240
D.12 Univariate Simulated Likelihood Estimator, a = 1.4. relative R.247
D.13 Univariate Simulated Likelihood Estimator, a = 1.3. fixed R.248
D.14 Univariate Simulated Likelihood Estimator, a = 1.3. relative R.249
D.15 Univariate Simulated Likelihood Estimator, a = 1.2. fixed R.250
D.10 Univariate Simulated Likelihood Estimator, a = 1.2. relative R.251
E.I BIAS for the Multivariate Simulated Likelihood Estimator, p = -0.9. 254
E.2 BIAS for the Multivariate Simulated Likelihood Estimator, p = -0.9 (cont) . 255
E.3 MSE for the Multivariate Simulated Likelihood Estimator, p = —0.9. 256
E.4 MSE for the Multivariate Simulated Likelihood Estimator, p = -0.9 (cont) . . 257
E.5 BIAS for the Multivariate Simulated Likelihood Estimator, p = -0.5. 258
E.O BIAS for the Multivariate Simulated Likelihood Estimator, p = -0.5 (cont) . 259
List of Tables
E.7 MSE for the Multivariate Simulated Likelihood Estimator, p = —0.5 .200
E.8 MSE for the Multivariate Simulated Likelihood Estimator, p = -0.9 (cont) . . 2G1
E.U BIAS for the Multivariate Simulated Likelihood Estimator, p = -0.1.202
E.10 BIAS for the Multivariate Simulated Likelihood Estimator, p = -0.1 (cont) . 203
E.ll MSE for the Multivariate Simulated Likelihood Estimator, p = -0.1 .2G4
E.12 MSE for the Multivariate Simulated Likelihood Estimator, p = -0.1 (cont) . . 265
E.13 BIAS for the Multivariate Simulated Likelihood Estimator, p = 0.0.200
E.14 BIAS for the Multivariate Simulated Likelihood Estimator, p = 0.0 (cont) . . 207
E.15 MSE for the Multivariate Simulated Likelihood Estimator, p = 0.0 .208
E.10 MSE for the Multivariate Simulated Likelihood Estimator, p = 0.0 (cont) . . . 209
F.I BIAS for the Constant Condition Covariation Estimators. R12 = -1.00 . 272
F.2 MSE for the Constant Condition Covariation Estimators. Ri2 = —1.00 . 273
F.3 BIAS for the Constant Condition Covariation Estimators. Rl2 = -0.50 . 274
F.4 MSE for the Constant Condition Covariation Estimators. Ri2 = -0.50 . 275
F.5 BIAS for the Constant Condition Covariation Estimators. Ri2 = 0.25.270
F.O MSE for the Constant Condition Covariation Estimators. Rl2 = 0.25.277
F.7 BIAS for the Constant Condition Covariation Estimators. Ri2 = 0.50.278
F.8 MSE for the Constant Condition Covariation Estimators. Rn = 0.50.279
F.9 BIAS for the Constant Condition Covariation Estimators. Rn = 1.00.280
F.10 MSE for the Constant Condition Covariation Estimators. Ru = 1.00.281
F.ll BIAS for the Constant Condition Covariation Estimators. Ru = 1.50.282
F.12 MSE for the Constant Condition Covariation Estimators. Ri2 = 1.50.283
G.I Univariate Estimation Results. Germany. AR(1). ,3 = 0.280
G.2 Univariate Estimation Results. Germany. AR(0). free 3.280
G.3 Univariate Estimation Results. Germany. AR(0). 3 = 0.280
G.4 Conditional Covariation Estimation Results. Germany. AR(0).287
G.5 VaR Coverage. MRP. Germany. AR(1). Constant Conditional Covariation . . 288
G.O VaR Coverage. MRP. Germany. AR(0). Constant Conditional Covariation . . 289
G.7 VaR Coverage. MRP. Germany. AR(0). Dynamic Conditional Covariation . . 289
G.8 VaR Coverage. EWP. Germany. AR(1). Constant Conditional Covariation . . 290
G.9 VaR Coverage. EWP. Germany. AR(0). Constant, Conditional Covariation . . 291
G.10 VaR Coverage. EWP, Germany. AR(0). Dynamic Conditional Covariation . . 291
G.ll Univariate Estimation Results, World, AR(1). free 3.293
G.12 Univariate Estimation Results, World. AR(1). /3 = 0.294
G.13 Univariate Estimation Results, World, AR(0). free 0.294
G.14 Univariate Estimation Results, World. AR(0). f3 = 0.295
G.15 Conditional Covariation Estimation Results. World, AR(0).297
List of Tables
G.16 VaR Coverage. MRP. World, AR(1). Constant Conditional Covariation . 301
G.17 VaR Coverage. MRP. World. AR(0). Constant Conditional Covariation . 301
G.18 VaR Coverage. MRP. World. AR(0). Dynamic Conditional Covariation . 303
G.19 VaR Coverage, EWP, World, AR(1). Constant Conditional Covariation . 304
G.20 VaR Coverage. EWP, World, AR(1). Dynamic Conditional Covariation . 304
G.21 VaR Coverage, EWP. World. AR(0). Constant Conditional Covariation . 305
G.22 VaR Coverage, EWP, World. AR(0). Dynamic Conditional Covariation . 305
G.23 The Dow Jones Stocks.307
G.24 Univariate Estimation Results, First Dow Jones, AR(1). free j3 .308
G.25 Univariate Estimation Results, First Dow Jones. AR(1). /? = 0.309
G.26 Univariate Estimation Results, First Dow Jones, AR(0), free (3 .311
G.27 Univariate Estimation Results, First Dow Jones, AR(0), /? = 0.313
G.28 Conditional Covariation Estimation Results, First Dow Jones, AR(1).315
G.29 Conditional Covariation Estimation Results, First Dow Jones, AR(0).316
G.30 VaR Coverage, MRP, First DJ, AR(1), Constant Conditional Covariation . . . 319
G.31 VaR Coverage, MRP, First DJ, AR(1). Dynamic Conditional Covariation . 319
G.32 VaR Coverage, MRP, First DJ, AR(0). Constant Conditional Covariation . 320
G.33 VaR Coverage, MRP, First DJ, AR(0), Dynamic Conditional Covariation . 321
G.34 VaR Coverage, EWP, First DJ, AR(1). Constant Conditional Covariation . . 322
G.35 VaR Coverage, EWP. First DJ, AR(1). Dynamic Conditional Covariation . 322
G.36 VaR Coverage. EWP. First DJ. AR(0), Constant Conditional Covariation . . 323
G.37 VaR Coverage. EWP. First DJ, AR(0), Dynamic Conditional Covariation . 323
G.38 Univariate Estimation Results. Second Dow Jones, AR(1), free /3.325
G.39 Univariate Estimation Results. Second Dow Jones, AR(1). 0 = 0.326
G.40 Univariate Estimation Results, Second Dow Jones, AR(0). free j3.327
G.41 Univariate Estimation Results. Second Dow Jones. AR(0). (5 - 0.329
G.42 Conditional Covariation Estimation Results. Second Dow Jones. AR(1) . 331
G.43 Conditional Covariation Estimation Results. Second Dow Jones. AR(0) . 332
G.44 VaR Coverage. MRP. Second DJ. AR(1). Constant Conditional Covariation . 334
G.45 VaR Coverage. MRP. Second DJ, AR(1). Dynamic Conditional Covariation . 334
G.46 VaR Coverage. MRP. Second DJ. AR(0). Constant Conditional Covariation . 335
G.47 VaR Coverage. MRP. Second DJ. AR(0). Dynamic Conditional Covariation . 33G
G.48 VaR Coverage. EWP. Second DJ. AR(1), Constant Conditional Covariation . 337
G.49 VaR Coverage. EWP. Second DJ. AR(1). Dynamic Conditional Covariation . 337
G.50 VaR Coverage. EWP, Second D.I. AR(0). Constant Conditional Covariation . 338
G.51 VaR Coverage. EWP, Second DJ, AR(0). Dynamic Conditional Covariation . 338
List of Figures
2.1 Discontinuity for q = 1 and j/0 . 9
2.2 Shape and Tail Behavior of Symmetric o stable Density Functions. 13
2.3 Shape of Asymmetric and Totally Right Skewed a stable Density Functions . 1G
2.4 Multivariate Density Functions Gaussian vs. Sub Gaussian. 33
2.5 Multivariate Density Contours Gaussian vs. Sub Gaussian. 34
3.1 Event Period Test Statistics. 5G
4.1 Asset, and Index Return Seri « . 78
4.2 Estimated Factor Scales. 80
4.3 Portfolio Weights. MRP. No Short Selling. 81
4.4 Portfolio Weights. MRP. Short Selling Allowed. 82
4.5 Empirical Downfall Probability Distribution. MRP. No Short Selling. 85
4.G Empirical Downfall Probability Distribution. MRP. Short Selling Allowed . . 87
4.7 Empirical Downfall Probability Distribution. EWP. 89
4.8 Transaction Cost Equivalents. MRP. No Short Selling. 90
4.9 Transaction Cost Equivalents. MRP. Short Selling Allowed . 91
5.1 BIAS for the Modified Empirical Estimator. 103
5.2 MSE for the Modified Empirical Estimator . 104
5.3 MSE of p" for the Modified Empirical Estimator . 105
5.4 Empirical Distribution and Descriptive Statistics for MADb. 11G
5.5 Empirical Distribution and Descriptive Statistics for MARDr. 118
5.G Empirical Distribution and Descriptive Statistics for OBfi. 120
5.7 Empirical Distribution and Descriptive Statistics for ORBH. 121
5.8 Empirical Distribution and Descriptive Statistics for OAD/(. 123
5.9 Empirical Distribution and Descriptive Statistics for ORDfl. 124
5.10 BIAS for the Univariate Simulated Likelihood Estimator. 127
5.11 Relative Efficiency for the Univariate Simulated Likelihood Estimator. 128
5.12 BIAS for the Multivariate Simulated Likelihood Estimator. 131
5.13 MSE for the Multivariate Simulated Likelihood Estimator. 132
List of Figures
5.14 MSE of p for the Mmtivariate Simulated Likelihood Estimator.133
6.1 Constant Conditional Covariation Estimators Comparison. BIAS.156
6.2 Constant Conditional Covariation Estimators Comparison. MSE.157
6.3 Germany Dataset Index and Return Series.170
6.4 World Dataset Index and Return Series.172
6.5 £( and Components, Germany. AR(1).178
6.6 Portfolio Weights. MRP. Germany. AR(1).179
6.7 Empirical Downfall Probabilities, MRP, Germany, AR(1), Dynamic Models . 181
6.8 Empirical Downfall Probabilities, EWP. Germany. AR(1). Dynamic Models . 183
6.9 Components of E,. World, AR(1).186
6.10 Empirical Downfall Probabilities, MRP, World, AR(1), Dynamic Models . 188
B.I BIAS for the Modified Empirical Estimator, p = -0.9 .204
B.2 MSE for the Modified Empirical Estimator, p = -0.9.206
B.3 BIAS for the Modified Empirical Estimator, p = -0.5 .208
B.4 MSE for the Modified Empirical Estimator, p = -0.5.210
B.5 BIAS for the Modified Empirical Estimator, p = -0.1 .212
B.6 MSE for the Modified Empirical Estimator, p = -0.1.214
B.7 BIAS for the Modified Empirical Estimator, p = 0.0 .216
B.8 MSE for the Modified Empirical Estimator, p = 0.0.218
G.I Parameter Restrictions, Germany, AR(1).285
G.2 Parameter Restrictions, Germany, AR(0).286
G.3 £( and Components. Germany. AR(0).287
G.4 Portfolio Weights. MRP. Germany. AR(0).288
G.5 Empirical Downfall Probabilities. MRP. Germany. AR(0), Dynamic Models . 290
G.6 Empirical Downfall Probabilities. EWP. Germany. AR(0). Dynamic Models . 292
G.7 Parameter Restrictions. World. AR(1).293
G.8 Parameter Restrictions. World. AR(0).295
G.9 £(. World. AR(1) .296
G.10 Et. World. AR(0) .298
G.ll Components of £,. World. AR(0).299
G.12 Portfolio Weights. MRP. World. AR(1).300
G.13 Portfolio Weights. MRP. World. AR(0).302
G.14 Empirical Downfall Probabilities, MRP, World. AR(0). Dynamic Models . 303
G.15 Empirical Downfall Probabilities. EWP. World, AR(1), Dynamic Models . 306
G.1C Empirical Downfall Probabilities. EWP. World. AR(0). Dynamic Models . 306
G.I7 Parameter Restrictions, First Dow Jones, AR(1) .309
G.18 Parameter Restrictions, First Dow Jones, AR(0) .312
List of Figures
G.l'J Empirical Downfall Probabilities. MRP. First D.I. AR(1). Dynamic Models . . 320
G.20 Empirical Downfall Probabilities. MRP. First D.I. AR(0). Dynamic Models . . 321
G.21 Empirical Downfall Probabilities. EWP. First D.I. AR(1). Dynamic Models . . 324
G.22 Empirical Downfall Probabilities. EWP. First D.I. AR(0). Dynamic Models . . 324
G.23 Parameter Restrictions. Second Dow Jones. AR(1) .32(i
G.24 Parameter Restrictions. Second Dow Jones. AR(0) .328
G.25 Empirical Downfall Probabilities. MRP. Second D.I. AR(1). Dynamic Models 335
G.20 Empirical Downfall Probabilities. MRP. Second D.I. AR(0). Dynamic Models 330
G.27 Empirical Downfall Probabilities. EWP. Second D.I. AR(1). Dynamic Models 339
G.28 Empirical Downfall Probabilities. EWP. Second D.I. AR(0). Dynamic Models 339 |
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| author | Hartz, Christoph |
| author_facet | Hartz, Christoph |
| author_role | aut |
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| ctrlnum | (OCoLC)229990674 (DE-599)BVBBV023223931 |
| discipline | Wirtschaftswissenschaften |
| discipline_str_mv | Wirtschaftswissenschaften |
| edition | 1. Aufl. |
| format | Thesis Book |
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| series2 | Quantitative Wirtschaftsforschung |
| spelling | Hartz, Christoph Verfasser aut α-stable random vectors with time varying spectral measure and applications to financial time series analysis Christoph Hartz [Alpha]-stable random vectors with time varying spectral measure and applications to financial time series analysis 1. Aufl. Berlin Pro Business 2008 XIV, 351 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantitative Wirtschaftsforschung Zugl.: München, Univ., Diss., 2008 Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Aktienrendite (DE-588)4126593-2 gnd rswk-swf Zufallsvektor (DE-588)4191098-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Aktienrendite (DE-588)4126593-2 s Zufallsvektor (DE-588)4191098-9 s Zeitreihenanalyse (DE-588)4067486-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016409781&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hartz, Christoph α-stable random vectors with time varying spectral measure and applications to financial time series analysis Zeitreihenanalyse (DE-588)4067486-1 gnd Aktienrendite (DE-588)4126593-2 gnd Zufallsvektor (DE-588)4191098-9 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4126593-2 (DE-588)4191098-9 (DE-588)4113937-9 |
| title | α-stable random vectors with time varying spectral measure and applications to financial time series analysis |
| title_alt | [Alpha]-stable random vectors with time varying spectral measure and applications to financial time series analysis |
| title_auth | α-stable random vectors with time varying spectral measure and applications to financial time series analysis |
| title_exact_search | α-stable random vectors with time varying spectral measure and applications to financial time series analysis |
| title_exact_search_txtP | α-stable random vectors with time varying spectral measure and applications to financial time series analysis |
| title_full | α-stable random vectors with time varying spectral measure and applications to financial time series analysis Christoph Hartz |
| title_fullStr | α-stable random vectors with time varying spectral measure and applications to financial time series analysis Christoph Hartz |
| title_full_unstemmed | α-stable random vectors with time varying spectral measure and applications to financial time series analysis Christoph Hartz |
| title_short | α-stable random vectors with time varying spectral measure and applications to financial time series analysis |
| title_sort | α stable random vectors with time varying spectral measure and applications to financial time series analysis |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd Aktienrendite (DE-588)4126593-2 gnd Zufallsvektor (DE-588)4191098-9 gnd |
| topic_facet | Zeitreihenanalyse Aktienrendite Zufallsvektor Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016409781&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hartzchristoph astablerandomvectorswithtimevaryingspectralmeasureandapplicationstofinancialtimeseriesanalysis AT hartzchristoph alphastablerandomvectorswithtimevaryingspectralmeasureandapplicationstofinancialtimeseriesanalysis |