GARCH-type Models with Generalized Secant Hyperbolic Innovations
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Paola Palmitesta
GARCH-type models have been analyzed assuming various nongaussian distributions of errors. In general, the asymmetric generalized Student-t random variable seems to be the distribution which better captures the nonnormality features of financial data. However, a drawback of this distribution is represented by the technical dificulties due to the evaluation of moments, especially in the case of fractional degrees of freedom. In this paper we propose to model high frequency time series returns using GARCH-type models with a generalized secant hyperbolic (GSH) distribution. The main advantage of the GSH distribution over the Student-t distribution is that all the moments are finite for each value of the shape parameter. The distribution is symmetric with respect to the mean, but we show that it is still possible to obtain the density in a closed form introducing a skewness parameter according to the method proposed by Fernandez and Steel. We use a Monte Carlo experiment to validate this distribution in the context of GARCH models with maximum likelihood estimates of parameters. Finally, we show an application to log returns of a stock index.
©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
