Bootstrapping Stationary ARMA-GARCH Models

1. Front Matter

   Pages I-XIII

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2. Introduction

   • Kenichi Shimizu

   Pages 1-7

3. Bootstrap Does not Always Work

   • Kenichi Shimizu

   Pages 9-17

4. Parametric AR(p)-ARCH(q) Models

   • Kenichi Shimizu

   Pages 19-64

5. Parametric ARMA(p, q)- GARCH(r, s) Models

   • Kenichi Shimizu

   Pages 65-83

6. Semiparametric AR(p)-ARCH(1) Models

   • Kenichi Shimizu

   Pages 85-126

7. Back Matter

   Pages 121-131

   PDF

Bootstrap technique is a useful tool for assessing uncertainty in statistical estimation and thus it is widely applied for risk management. Bootstrap is without doubt a promising technique, however, it is not applicable to all time series models. A wrong application could lead to a false decision to take too much risk.

Kenichi Shimizu investigates the limit of the two standard bootstrap techniques, the residual and the wild bootstrap, when these are applied to the conditionally heteroscedastic models, such as the ARCH and GARCH models. The author shows that the wild bootstrap usually does not work well when one estimates conditional heteroscedasticity of Engle’s ARCH or Bollerslev’s GARCH models while the residual bootstrap works without problems. Simulation studies from the application of the proposed bootstrap methods are demonstrated together with the theoretical investigation.

• Bootstrapping
• RM
• Risk modelling
• Time series
• bootstrap methods
• conditionally heteroscedastic models
• mathematical statistics
• risk management
• time series analysis

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

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