Garch Models: Structure, Statistical Inference and Financial Applications

by Christian Francq (Laboratory EQUIPPE, Lille, France); Jean-Michel Zakoian (Laboratory EQUIPPE, Lille, France)

• ISBN13: 9780470670040
• ISBN10: 0470670045
• Format: eBook
• Copyright: 2010-06-01
• Publisher: Wiley

Summary

This book provides a complete coverage to GARCH modeling, including probability properties, identifying an appropriate model, estimation and testing, multivariate extensions including EGARCH, TGARCH and APGARCH, volatility features such as asymmetries and financial applications.Many sections are based on up to date research, featured in econometric and statistic journals. GARCH models is accessible to a wide audience who have worked in time series analysis and wish to become familiar with the use and modeling techniques specially devoted to financial time series.

Table of Contents

Preface

Notation

Classical Time Series Models and Financial Series

Stationary Processes

ARMA and ARIMA Models

Financial Series

Random Variance Models

Bibliographical Notes

Exercises

Univariate GARCH Models

GARCH( p, q ) Processes

Definitions and Representations

Stationarity Study

ARCH ( ∞ ) Representation

Properties of the Marginal Distribution

Autocovariances of the Squares of a GARCH

Theoretical Predictions

Bibliographical Notes

Exercises

Mixing

Markov Chains with Continuous State Space

Mixing Properties of GARCH Processes

Bibliographical Notes

Exercises

Temporal Aggregation and Weak GARCH Models

Temporal Aggregation of GARCH Processes

Weak GARCH

Aggregation of Strong GARCH Processes in the Weak GARCH Class

Bibliographical Notes

Exercises

Statistical Inference

Identification

Autocorrelation Check for White Noise

Identifying the ARMA Orders of an ARMA-GARCH

Identifying the GARCH Orders of an ARMA-GARCH Model

Lagrange Multiplier Test for Conditional Homoscedasticity

Application to Real Series

Bibliographical Notes

Exercises

Estimating ARCH Models by Least Squares

Estimation of ARCH( q ) models by Ordinary Least Squares

Estimation of ARCH( q ) Models by Feasible Generalized Least Squares

Estimation by Constrained Ordinary Least Squares

Bibliographical Notes

Exercises

Estimating GARCH Models by Quasi-Maximum Likelihood

Conditional Quasi-Likelihood

Estimation of ARMA-GARCH Models by Quasi-Maximum Likelihood

Application to Real Data

Proofs of the Asymptotic Results

Bibliographical Notes

Exercises

Tests Based on the Likelihood

Test of the Second-Order Stationarity Assumption

Asymptotic Distribution of the QML When ¿ 0 is at the Boundary

Significance of the GARCH Coefficients

Diagnostic Checking with Portmanteau Tests

Application: Is the GARCH(1,1) Model Overrepresented?

Proofs of the Main Results

Bibliographical Notes

Exercises

Optimal Inference and Alternatives to the QMLE

Maximum Likelihood Estimator

Maximum Likelihood Estimator with Misspecified Density

Alternative Estimation Methods

Bibliographical Notes

Exercises

Extensions and Applications

Asymmetries

Exponential GARCH Model

Threshold GARCH Model

Asymmetric Power GARCH Model

Other Asymmetric GARCH Models

A GARCH Model with Contemporaneous Conditional Asymmetry

Empirical Comparisons of Asymmetric GARCH Formulations

Bibliographical Notes

Exercises

Multivariate GARCH Processes

Multivariate Stationary Processes

Multivariate GARCH Models

Stationarity

Estimation of the CCC Model

Bibliographical Notes

Exercises

Financial Applications

Relation between GARCH and Continuous-Time Models

Option Pricing

Value at Risk and Other Risk Measures

Bibliographical Notes

Exercises

Appendices

Ergodicity, Martingales, Mixing

Ergodicity

Martingale Increments

Mixing

Autocorrelation and Partial Autocorrelation

Partial Autocorrelation

Generalized Bartlett Formula for Nonlinear Processes

Solutions to the Exercises

Problems

References

Index

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