Prologue.Notation. 1 What is an ARCH process?
1.1 Introduction.
1.2 The Autoregressive Conditionally Heteroskedastic Process.
1.3 The Leverage Effect.
1.4 The Non-trading Period Effect.
1.5 Non-synchronous Trading Effect.
1.6 The Relationship between Conditional Variance and Conditional Mean. 2 ARCH Volatility Specifications.
2.1 Model Specifications.
2.2 Methods of Estimation.
2.3. Estimating the GARCH Model with EViews 6: An Empirical Example..
2.4. Asymmetric Conditional Volatility Specifications.
2.5. Simulating ARCH Models Using EViews.
2.6. Estimating Asymmetric ARCH Models with G@RCH 4.2 OxMetrics – An Empirical Example..
2.7. Misspecification Tests.
2.8 Other ARCH Volatility Specifications.
2.9 Other Methods of Volatility Modeling.
2.10 Interpretation of the ARCH Process. 3 Fractionally Integrated ARCH Models.
3.1 Fractionally Integrated ARCH Model Specifications.
3.2 Estimating Fractionally Integrated ARCH Models Using G@RCH 4.2 OxMetrics – An Empirical Example.
3.3 A More Detailed Investigation of the Normality of the Standardized Residuals – Goodness-of-fit Tests. 4 Volatility Forecasting: An Empirical Example Using EViews 6.
4.1 One-step-ahead Volatility Forecasting.
4.2 Ten-step-ahead Volatility Forecasting. 5 Other Distributional Assumptions.
5.1 Non-Normally Distributed Standardized Innovations.
5.2 Estimating ARCH Models with Non-Normally Distributed Standardized Innovations Using G@RCH 4.2 OxMetrics – An Empirical Example.
5.3 Estimating ARCH Models with Non-Normally Distributed Standardized Innovations Using EViews 6 – An Empirical Example.
5.4 Estimating ARCH Models with Non-Normally Distributed Standardized Innovations Using EViews 6 – The LogL Object. 6 Volatility Forecasting: An Empirical Example Using G@RCH Ox. 7 Intra-Day Realized Volatility Models.
7.1 Realized Volatility.
7.2 Intra-Day Volatility Models.
7.3 Intra-Day Realized Volatility & ARFIMAX Models in G@RCH 4.2 OxMetrics – An Empirical example. 8 Applications in Value-at-Risk, Expected Shortfalls, Options Pricing.
8.1 One-day-ahead Value-at-Risk Forecasting.
8.2 One-day-ahead Expected Shortfalls Forecasting.
8.3 FTSE100 Index: One-step-ahead Value-at-Risk and Expected Shortfall Forecasting.
8.4 Multi-period Value-at-Risk and Expected Shortfalls Forecasting.
8.5 ARCH Volatility Forecasts in Black and Scholes Option Pricing.
8.6 ARCH Option Pricing Formulas. 9 Implied Volatility Indices and ARCH Models.
9.1 Implied Volatility.
9.2 The VIX Index.
9.3 The Implied Volatility Index as an Explanatory Variable.
9.4 ARFIMAX Modeling for Implied Volatility Index. 10 ARCH Model Evaluation and Selection.
10.1 Evaluation of ARCH Models.
10.2 Selection of ARCH Models.
10.3 Application of Loss Functions as Methods of Model Selection..
10.4 The SPA Test for VaR and Expected Shortfalls. 11 Multivariate ARCH Models.
11.1 Model Specifications.
11.2 Maximum Likelihood Estimation.
11.3 Estimating Multivariate ARCH Models Using EViews 6.
11.4 Estimating Multivariate ARCH Models Using G@RCH 5.0.
11.5 Evaluation of Multivariate ARCH Models.
References.
Author Index.
Subject Index.
Preface.Notation. 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. 2 GARCH(p, q) Processes.
2.1 Definitions and Representations.
2.2 Stationarity Study.
2.3 ARCH (∞) Representation.
2.4 Properties of the Marginal Distribution.
2.5 Autocovariances of the Squares of a GARCH.
2.6 Theoretical Predictions.
2.7 Bibliographical Notes.
2.8 Exercises. 3 Mixing.
3.1 Markov Chains with Continuous State Space.
3.2 Mixing Properties of GARCH Processes.
3.3 Bibliographical Notes.
3.4 Exercises. 4 Temporal Aggregation and Weak GARCH Models.
4.1 Temporal Aggregation of GARCH Processes.
4.2 Weak GARCH.
4.3 Aggregation of Strong GARCH Processes in the Weak GARCH Class.
4.4 Bibliographical Notes.
4.5 Exercises. Part II Statistical Inference. 5 Identification.
5.1 Autocorrelation Check for White Noise.
5.2 Identifying the ARMA Orders of an ARMA-GARCH.
5.3 Identifying the GARCH Orders of an ARMA-GARCH Model.
5.4 Lagrange Multiplier Test for Conditional Homoscedasticity.
5.5 Application to Real Series.
5.6 Bibliographical Notes.
5.7 Exercises. 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 Generalized Least Squares.
6.3 Estimation by Constrained Ordinary Least Squares.
6.4 Bibliographical Notes.
6.5 Exercises. 7 Estimating GARCH Models by Quasi-Maximum Likelihood.
7.1 Conditional Quasi-Likelihood.
7.2 Estimation of ARMA-GARCH Models by Quasi-Maximum Likelihood.
7.3 Application to Real Data.
7.4 Proofs of the Asymptotic Results.
7.5 Bibliographical Notes.
7.6 Exercises. 8 Tests Based on the Likelihood.
8.1 Test of the Second-Order Stationarity Assumption.
8.2 Asymptotic Distribution of the QML When θ0 is at the Boundary.
8.3 Significance of the GARCH Coefficients.
8.4 Diagnostic Checking with Portmanteau Tests.
8.5 Application: Is the GARCH(1,1) Model Overrepresented?
8.6 Proofs of the Main Results.
8.7 Bibliographical Notes.
8.8 Exercises. 9 Optimal Inference and Alternatives to the QMLE.
9.1 Maximum Likelihood Estimator.
9.2 Maximum Likelihood Estimator with Misspecified Density.
9.3 Alternative Estimation Methods.
9.4 Bibliographical Notes.
9.5 Exercises. Part III Extensions and Applications.
10 Asymmetries.
10.1 Exponential GARCH Model.
10.2 Threshold GARCH Model.
10.3 Asymmetric Power GARCH Model.
10.4 Other Asymmetric GARCH Models.
10.5 A GARCH Model with Contemporaneous Conditional Asymmetry.
10.6 Empirical Comparisons of Asymmetric GARCH Formulations.
10.7 Bibliographical Notes.
10.8 Exercises. 11 Multivariate GARCH Processes.
11.1 Multivariate Stationary Processes.
11.2 Multivariate GARCH Models.
11.3 Stationarity.
11.4 Estimation of the CCC Model.
11.5 Bibliographical Notes.
11.6 Exercises. 12 Financial Applications.
12.1 Relation between GARCH and Continuous-Time Models.
12.2 Option Pricing.
12.3 Value at Risk and Other Risk Measures.
12.4 Bibliographical Notes.
12.5 Exercises. Part IV Appendices.
A Ergodicity, Martingales, Mixing.
A.1 Ergodicity.
A.2 Martingale Increments.
A.3 Mixing.
B Autocorrelation and Partial Autocorrelation.
B.1 Partial Autocorrelation.
B.2 Generalized Bartlett Formula for Nonlinear Processes.
C Solutions to the Exercises.
D Problems. References. Index.
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