GARCH models : structure, statistical inference and financial applications / Christian Francq, Jean-Michel Zakoian.

Cover; Title Page; Copyright; Contents; Chapter 1 Classical Time Series Models and Financial Series; 1.1 Stationary Processes; 1.2 ARMA and ARIMA Models; 1.3 Financial Series; 1.4 Random Variance Models; 1.5 Bibliographical Notes; 1.6 Exercises; Part I Univariate GARCH Models; Chapter 2 GARCH(p, q) Processes; 2.1 Definitions and Representations; 2.2 Stationarity Study; 2.2.1 The GARCH(1,1) Case; 2.2.2 The General Case; 2.3 ARCH(∞) Representation*; 2.3.1 Existence Conditions; 2.3.2 ARCH(∞) Representation of a GARCH; 2.3.3 Long-Memory ARCH; 2.4 Properties of the Marginal Distribution

2.4.1 Even-Order Moments2.4.2 Kurtosis; 2.5 Autocovariances of the Squares of a GARCH; 2.5.1 Positivity of the Autocovariances; 2.5.2 The Autocovariances Do Not Always Decrease; 2.5.3 Explicit Computation of the Autocovariances of the Squares; 2.6 Theoretical Predictions; 2.7 Bibliographical Notes; 2.8 Exercises; Chapter 3 Mixing*; 3.1 Markov Chains with Continuous State Space; 3.2 Mixing Properties of GARCH Processes; 3.3 Bibliographical Notes; 3.4 Exercises; Chapter 4 Alternative Models for the Conditional Variance; 4.1 Stochastic Recurrence Equation (SRE); 4.2 Exponential GARCH Model

4.3 Log-GARCH Model4.3.1 Stationarity of the Extended Log-GARCH Model; 4.3.2 Existence of Moments and Log-Moments; 4.3.3 Relations with the EGARCH Model; 4.4 Threshold GARCH Model; 4.5 Asymmetric Power GARCH Model; 4.6 Other Asymmetric GARCH Models; 4.7 A GARCH Model with Contemporaneous Conditional Asymmetry; 4.8 Empirical Comparisons of Asymmetric GARCH Formulations; 4.9 Models Incorporating External Information; 4.10 Models Based on the Score: GAS and Beta-t-(E)GARCH; 4.11 GARCH-type Models for Observations Other Than Returns; 4.12 Complementary Bibliographical Notes; 4.13 Exercises

Part II Statistical InferenceChapter 5 Identification; 5.1 Autocorrelation Check for White Noise; 5.1.1 Behaviour of the Sample Autocorrelations of a GARCH Process; 5.1.2 Portmanteau Tests; 5.1.3 Sample Partial Autocorrelations of a GARCH; 5.1.4 Numerical Illustrations; 5.2 Identifying the ARMA Orders of an ARMA-GARCH; 5.2.1 Sample Autocorrelations of an ARMA-GARCH; 5.2.2 Sample Autocorrelations of an ARMA-GARCH Process When the Noise is Not Symmetrically Distributed; 5.2.3 Identifying the Orders (P, Q); 5.3 Identifying the GARCH Orders of an ARMA-GARCH Model

5.3.1 Corner Method in the GARCH Case5.3.2 Applications; 5.4 Lagrange Multiplier Test for Conditional Homoscedasticity; 5.4.1 General Form of the LM Test; 5.4.2 LM Test for Conditional Homoscedasticity; 5.5 Application to Real Series; 5.6 Bibliographical Notes; 5.7 Exercises; Chapter 6 Estimating ARCH Models by Least Squares; 6.1 Estimation of ARCH(q) models by Ordinary Least Squares; 6.2 Estimation of ARCH(q) Models by Feasible Generalised Least Squares; 6.3 Estimation by Constrained Ordinary Least Squares; 6.3.1 Properties of the Constrained OLS Estimator