| Introduction | p. 1 |
| A Very Brief History of Financial Time Series | p. 1 |
| Contents of the Monograph | p. 3 |
| Parameter Estimation in a General Conditionally Heteroscedastic Time Series Model | p. 4 |
| Whittle Estimation in GARCH(1,1) | p. 10 |
| Structure of the Monograph | p. 11 |
| Some Mathematical Tools | p. 13 |
| Stationarity and Ergodicity | p. 13 |
| Uniform Convergence via the Ergodic Theorem | p. 17 |
| Bochner Expectation | p. 19 |
| The Ergodic Theorem for Sequences of B-valued Random Elements | p. 22 |
| Matrix Norms | p. 23 |
| Weak Convergence in <$>{op C}<$>(K,<$>{op R}^{dprime}<$>) | p. 24 |
| Exponentially Fast Almost Sure Convergence | p. 26 |
| Stochastic Recurrence Equations | p. 29 |
| Financial Time Series: Facts and Models | p. 37 |
| Stylized Facts of Financial Log-return Data | p. 39 |
| Uncorrelated Observations | p. 39 |
| Time-varying Volatility (Conditional Heteroscedasticity) | p. 41 |
| Heavy-tailed and Asymmetric Unconditional Distribution | p. 41 |
| Leverage Effects | p. 43 |
| ARMA Models | p. 44 |
| Conditionally Heteroscedastic Time Series Models | p. 48 |
| AG ARCH Models | p. 48 |
| EGARCH Models | p. 60 |
| Stochastic Volatility Models | p. 61 |
| Parameter Estimation: An Overview | p. 63 |
| Estimation for ARM A Processes | p. 63 |
| Gaussian Quasi Maximum Likelihood Estimation | p. 63 |
| Least-squares Estimation | p. 68 |
| Whittle Estimation | p. 69 |
| Estimation for GARCH Processes | p. 72 |
| Quasi Maximum Likelihood Estimation | p. 73 |
| Whittle Estimation | p. 79 |
| Quasi Maximum Likelihood Estimation in ConditionallyHeteroscedastic Time Series Models: A StochasticRecurrence Equations Approach | p. 85 |
| Overview | p. 85 |
| Stationarity, Ergodicity and Invertibility | p. 87 |
| Existence of a Stationary Solution | p. 88 |
| Invertibility | p. 92 |
| Definition of the Function ht | p. 97 |
| Consistency of the QMLE | p. 99 |
| Examples: Consistency | p. 102 |
| EGARCH | p. 102 |
| AGARCH(p,q) | p. 105 |
| The First and Second Derivatives of ht and ht | p. 110 |
| Asymptotic Normality of the QMLE | p. 116 |
| Examples: Asymptotic Normality | p. 120 |
| AGARCH(p,q) | p. 120 |
| EGARCH | p. 124 |
| Non-Stationarities | p. 131 |
| Fitting AGARCH(1,1) to the NYSE Composite Data | p. 131 |
| A Simulation Study | p. 132 |
| Maximum Likelihood Estimation in Conditionally Heteroscedastic Time Series Models | p. 141 |
| Consistency of the MLE | p. 143 |
| Main Result | p. 143 |
| Consistency of the MLE with Respect to Student t Innovations | p. 146 |
| Misspecification of the Innovations Density | p. 148 |
| Inconsistency of the MLE | p. 148 |
| Misspecfication of <$>{cal D}<$> in the GARCH(p,q) Model | p. 154 |
| Asymptotic Normality of the MLE | p. 157 |
| Asymptotic Normality of the MLE with Respect to Student t Innovations | p. 165 |
| Quasi Maximum Likelihood Estimation in a Generalized Conditionally Heteroscedastic Time Series Model with Heavy-tailed Innovations | p. 169 |
| Stable Limits of Infinite Variance Martingale Transforms | p. 170 |
| Infinite Variance Stable Limits of the QMLE | p. 172 |
| Limit Behavior of the QMLE in GARCH(p,q) with Heavy-tailed Innovations | p. 175 |
| Verification of Strong Mixing with Geometric Rate of (Yt) in GARCH(p,q) | p. 179 |
| Whittle Estimation in a Heavy-tailed GARCH(1,1) Model | p. 187 |
| Introduction | p. 187 |
| Limit Theory for the Sample Autocovariance Function | p. 189 |
| Main Results | p. 191 |
| Excursion: Yule-Walker Estimation in ARCH(p) | p. 194 |
| Proof of Theorem 8.3.1 | p. 195 |
| Proof of Theorem 8.3.2 | p. 200 |
| References | p. 215 |
| Author Index | p. 221 |
| Index | p. 225 |
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