Clusters of Extreme Observations and Extremal Index Estimate in GARCH Processes
Several methods have been proposed for identifying clusters of extreme values leading to estimators of the extremal index; the latter represents,in the limit, the mean-size of each cluster of thresholds exceedances. The detection of clusters of extremes is relevant for the class of processes commonly used in financial econometrics, such as GARCH processes. The paper illustrates a novel approach to the above identification that exploits additional knowledge of the trajectory of the process around extreme events, and compares it to traditional approaches, using simulation from a GARCH process. We assess the relative performance of estimators in terms of bias, mean square error and distributional properties.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
Articles in the same Issue
- Article
- Introduction
- Extensions of the Forward Search to Time Series
- Analyzing Financial Time Series through Robust Estimators
- Clusters of Extreme Observations and Extremal Index Estimate in GARCH Processes
- Estimating Stochastic Volatility Models: A Comparison of Two Importance Samplers
- MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model
- GARCH-type Models with Generalized Secant Hyperbolic Innovations
- Mixture Processes for Financial Intradaily Durations
- Constructing Non-linear Gaussian Time Series by Means of a Simplified State Space Representation
- Statistical Tests for Lyapunov Exponents of Deterministic Systems
- Assessing Chaos in Time Series: Statistical Aspects and Perspectives
- On the Stationarity of First-order Nonlinear Time Series Models: Some Developments
- Experimental Design for Time-Dependent Models with Correlated Observations
- Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation
- Stability and Consistency of Seasonally Adjusted Aggregates and Their Component Patterns
- Seasonal Specific Structural Time Series
- Relationship between Local and Global Nonparametric Estimators Measures of Fitting and Smoothing
Articles in the same Issue
- Article
- Introduction
- Extensions of the Forward Search to Time Series
- Analyzing Financial Time Series through Robust Estimators
- Clusters of Extreme Observations and Extremal Index Estimate in GARCH Processes
- Estimating Stochastic Volatility Models: A Comparison of Two Importance Samplers
- MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model
- GARCH-type Models with Generalized Secant Hyperbolic Innovations
- Mixture Processes for Financial Intradaily Durations
- Constructing Non-linear Gaussian Time Series by Means of a Simplified State Space Representation
- Statistical Tests for Lyapunov Exponents of Deterministic Systems
- Assessing Chaos in Time Series: Statistical Aspects and Perspectives
- On the Stationarity of First-order Nonlinear Time Series Models: Some Developments
- Experimental Design for Time-Dependent Models with Correlated Observations
- Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation
- Stability and Consistency of Seasonally Adjusted Aggregates and Their Component Patterns
- Seasonal Specific Structural Time Series
- Relationship between Local and Global Nonparametric Estimators Measures of Fitting and Smoothing
