GARCH Models: Structure, Statistical Inference and Financial Applications

GARCH Models: Structure, Statistical Inference and Financial Applications

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Provides a comprehensive and updated study of GARCH models and their applications in finance, covering new developments in the discipline

This book provides a comprehensive and systematic approach to understanding GARCH time series models and their applications whilst presenting the most advanced results concerning the theory and practical aspects of GARCH. The probability structure of standard GARCH models is studied in detail as well as statistical inference such as identification, estimation, and tests. The book also provides new coverage of several extensions such as multivariate models, looks at financial applications, and explores the very validation of the models used.

GARCH Models: Structure, Statistical Inference and Financial Applications, 2nd Edition features a new chapter on Parameter-Driven Volatility Models, which covers Stochastic Volatility Models and Markov Switching Volatility Models. A second new chapter titled Alternative Models for the Conditional Variance contains a section on Stochastic Recurrence Equations and additional material on EGARCH, Log-GARCH, GAS, MIDAS, and intraday volatility models, among others. The book is also updated with a more complete discussion of multivariate GARCH; a new section on Cholesky GARCH; a larger emphasis on the inference of multivariate GARCH models; a new set of corrected problems available online; and an up-to-date list of references.

  • Features up-to-date coverage of the current research in the probability, statistics, and econometric theory of GARCH models
  • Covers significant developments in the field, especially in multivariate models
  • Contains completely renewed chapters with new topics and results
  • Handles both theoretical and applied aspects
  • Applies to researchers in different fields (time series, econometrics, finance)
  • Includes numerous illustrations and applications to real financial series
  • Presents a large collection of exercises with corrections
  • Supplemented by a supporting website featuring R codes, Fortran programs, data sets and Problems with corrections

GARCH Models, 2nd Edition is an authoritative, state-of-the-art reference that is ideal for graduate students, researchers, and practitioners in business and finance seeking to broaden their skills of understanding of econometric time series models.

Product Details

ISBN-13: 9781119313489
Publisher: Wiley
Publication date: 03/21/2019
Sold by: Barnes & Noble
Format: NOOK Book
Pages: 504
File size: 28 MB
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About the Author

CHRISTIAN FRANCQ, PHD, is Professor of Econometrics and Finance at CREST (Center for Research in Economics and Statistics) and ENSAE (National School of Statistics and Economic Administration).

JEAN-MICHEL ZAKOIAN, PHD, is Professor of Econometrics and Finance at CREST (Center for Research in Economics and Statistics) and ENSAE (National School of Statistics and Economic Administration).

They have both published various papers on this topic in statistical and econometric journals, including Econometrica, Econometric Theory, Journal of Econometrics, Bernoulli, Journal of the Royal Statistical Society (Series B) and Journal of the American Statistical Association.

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Table of Contents



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.



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“This book is very well written and a joy to read. The style of presentation makes it an excellent text for advanced graduate students and researchers alike.” (JASA, 1 June 2012)

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