GARCH models : structure, statistical inference and financial applications

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 Moments -- 2.4.2 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 Model -- 4.3.1 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.