Bootstrapping Stationary ARMA-GARCH Models (eBook)

Kenichi Shimizu (Autor)

eBook Download: PDF

2010 | 2010
148 Seiten
Vieweg & Teubner (Verlag)
978-3-8348-9778-7 (ISBN)

Infos

Dr. Kenichi Shimizu completed his doctoral thesis at the Department of Mathematics at the Technical University, Braunschweig.

Inhalt

Geleitwort 7
Acknowledgements 9
Contents 10
List o igures 12
1 Introduction 13
1.1 Financial Time Series and the GARCH Model 13
1.2 The Limit of the Classical Statistical Analysis 15
1.3 An Alternative Approach: the Bootstrap Techniques 17
1.4 Structure of the Book 19
2 Bootstrap Does not Always Work 20
2.1 Estimation of Heteroscedasticity and Bootstrap 21
2.1.1 Simple Residual Bootstrap Does not Work 21
2.1.2 Wild Bootstrap Usually Does not Work 23
2.2 Result of a False Application: the VaR Model 24
2.2.1 VaR Model 25
2.2.2 Simulations 26
3 Parametric AR(p)-ARCH(q) Models 29
3.1 Estimation Theory 29
3.1.1 Model and Assumptions 30
3.1.2 OLS Estimation 32
3.1.2.1 AR part 33
3.1.2.2 ARCH part 37
3.2 Residual Bootstrap 47
3.3 Wild Bootstrap 62
3.4 Simulations 70
4 Parametric ARMA(p, q)GARCH(r, s) Models 75
4.1 Estimation Theory 75
4.1.1 Model and Assumptions 76
4.1.2 QML Estimation 77
4.2 Residual Bootstrap 78
4.3 Wild Bootstrap 86
4.4 Simulations 90
5 Semiparametric AR(p)-ARCH(1) Models 94
5.1 Estimation Theory 94
5.1.1 Model and Assumptions 95
5.1.2 NW Estimation 96
5.1.2.1 The imaginary case where ?t are known 97
5.1.2.2 The standard case where ?t are unknown 98
5.2 Residual Bootstrap 107
5.3 Wild Bootstrap 124
5.4 Simulations 126
Appendix 129
A Central Limit Theorems 130
B Miscellanea 132
Bibliography 134
Index 137

Produkt-Details

• Erscheint lt. Verlag: 1.11.2010
• Zusatzinfo: 148 p. 12 illus.
• Verlagsort: Wiesbaden
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: bootstrap methods • Bootstrapping • conditionally heteroscedastic models • Mathematical Statistics • Risk Management • risk modelling • RM • Time Series • Time Series Analysis
• ISBN-10: 3-8348-9778-7 / 3834897787
• ISBN-13: 978-3-8348-9778-7 / 9783834897787