GARCH Models: Structure, Statistical Inference and Financial Applications
GARCH Models: Structure, Statistical Inference and Financial Applications
复制标题
DOI：
10.1002/9780470670057
复制
发表时间：
2010-08
影响因子：
1.9
通讯作者：
C. Francq;J. Zakoian
中科院分区：
文献类型：
--
作者：
C. Francq;J. Zakoian
前言。符号。1经典时间序列模型和金融序列。1.1平稳过程。1.2 ARMA和ARIMA模型。1.3金融序列。1.4随机方差模型。1.5参考书目注释。1.6习题。第一部分单变量GARCH模型。2 GARCH（p, q）过程。2.1定义与表示。2.2平稳性研究。2.3 ARCH（）表示。2.4边际分布的性质。2.5 GARCH平方的自协方差。2.6理论预测。2.7参考书目注释。2.8习题。3混合。3.1连续状态空间的马尔可夫链。3.2 GARCH过程的混合特性。3.3参考书目注释。3.4习题。4时间聚集和弱GARCH模型。4.1 GARCH过程的时间聚集。4.2弱GARCH。4.3弱GARCH类中强GARCH过程的聚合。4.4参考书目注释。4.5练习。第二部分统计推断。5辨识。5.1白噪声的自相关检验。5.2辨识ARMA- garch的ARMA阶数。5.3确定ARMA-GARCH模型的GARCH阶数。5.4条件均方差的拉格朗日乘数检验。5.5在实数序列中的应用。5.6参考书目。5.7习题。6用最小二乘估计ARCH模型。6.1用普通最小二乘估计ARCH(q)模型。6.2用可行广义最小二乘估计ARCH(q)模型。6.3用约束普通最小二乘估计。6.4参考书目。6.5习题。7用7.1条件拟似然。7.2 ARMA-GARCH模型的拟极大似然估计。7.3在实际数据中的应用。7.4渐近结果的证明。7.5参考文献注释。7.6习题。8基于似然的检验。8.1二阶平稳性假设的检验。8.2边界为0时QML的渐近分布。8.3 GARCH系数的显著性。8.4 Portmanteau检验的诊断检验。8.5应用：GARCH（1,1）模型是否被过度表示？8.6主要结果的证明。8.7参考书目注释。8.8习题。9 QMLE的最优推理和替代。9.1最大似然估计量。9.2密度错误的最大似然估计量。9.3可选的估计方法。9.4参考书目注释。9.5练习。第三部分的扩展和应用。10不对称。10.1指数GARCH模型。10.2阈值GARCH模型。10.3非对称功率GARCH模型。10.4其他非对称GARCH模型。10.5具有同期条件不对称的GARCH模型。10.6非对称GARCH公式的经验比较。10.7参考文献注释。10.8练习。11多元GARCH过程。11.1多元平稳过程。11.2多元GARCH模型。11.3平稳性。11.4CCC模型。11.5参考书目。11.6练习。12金融应用。12.1 GARCH与连续时间模型的关系。12.2期权定价。12.3风险价值和其他风险度量。12.4参考书目。12.5练习。第四部分附录。A遍历性，鞅，混合。背书的遍历性。A.2鞅增量。由混合。B自相关和部分自相关。B.1部分自相关。B.2非线性过程的广义Bartlett公式。C练习题解答。D问题。参考文献。索引。
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 0 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.