GARCH Models, 2nd Edition

GARCH Models, 2nd Edition

by Christian Francq, Jean-Michel Zakoian
Released June 2019
Publisher(s): Wiley
ISBN: 9781119313571

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Book description

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.

Table of contents

  1. Cover
  2. Preface to the Second Edition
  3. Preface to the First Edition
  4. Notation
  5. 1 Classical Time Series Models and Financial Series
    1. 1.1 Stationary Processes
    2. 1.2 ARMA and ARIMA Models
    3. 1.3 Financial Series
    4. 1.4 Random Variance Models
    5. 1.5 Bibliographical Notes
    6. 1.6 Exercises
  6. Part I: Univariate GARCH Models
    1. 2 GARCH(p, q) Processes
      1. 2.1 Definitions and Representations
      2. 2.2 Stationarity Study
      3. 2.3 ARCH(∞)Representation
      4. 2.4 Properties of the Marginal Distribution
      5. 2.5 Autocovariances of the Squares of a GARCH
      6. 2.6 Theoretical Predictions
      7. 2.7 Bibliographical Notes
      8. 2.8 Exercises
    2. 3 Mixing*
      1. 3.1 Markov Chains with Continuous State Space
      2. 3.2 Mixing Properties of GARCH Processes
      3. 3.3 Bibliographical Notes
      4. 3.4 Exercises
    3. 4 Alternative Models for the Conditional Variance
      1. 4.1 Stochastic Recurrence Equation (SRE)
      2. 4.2 Exponential GARCH Model
      3. 4.3 Log‐GARCH Model
      4. 4.4 Threshold GARCH Model
      5. 4.5 Asymmetric Power GARCH Model
      6. 4.6 Other Asymmetric GARCH Models
      7. 4.7 A GARCH Model with Contemporaneous Conditional Asymmetry
      8. 4.8 Empirical Comparisons of Asymmetric GARCH Formulations
      9. 4.9 Models Incorporating External Information
      10. 4.10 Models Based on the Score: GAS and Beta‐t‐(E)GARCH
      11. 4.11 GARCH‐type Models for Observations Other Than Returns
      12. 4.12 Complementary Bibliographical Notes
      13. 4.13 Exercises
  7. Part II: Statistical Inference
    1. 5 Identification
      1. 5.1 Autocorrelation Check for White Noise
      2. 5.2 Identifying the ARMA Orders of an ARMA‐GARCH
      3. 5.3 Identifying the GARCH Orders of an ARMA‐GARCH Model
      4. 5.4 Lagrange Multiplier Test for Conditional Homoscedasticity
      5. 5.5 Application to Real Series
      6. 5.6 Bibliographical Notes
      7. 5.7 Exercises
    2. 6 Estimating ARCH Models by Least Squares
      1. 6.1 Estimation of ARCH( q ) models by Ordinary Least Squares
      2. 6.2 Estimation of ARCH( q ) Models by Feasible Generalised Least Squares
      3. 6.3 Estimation by Constrained Ordinary Least Squares
      4. 6.4 Bibliographical Notes
      5. 6.5 Exercises
    3. 7 Estimating GARCH Models by Quasi‐Maximum Likelihood
      1. 7.1 Conditional Quasi‐Likelihood
      2. 7.2 Estimation of ARMA–GARCH Models by Quasi‐Maximum Likelihood
      3. 7.3 Application to Real Data
      4. 7.4 Proofs of the Asymptotic Results*
      5. 7.5 Bibliographical Notes
      6. 7.6 Exercises
    4. 8 Tests Based on the Likelihood
      1. 8.1 Test of the Second‐Order Stationarity Assumption
      2. 8.2 Asymptotic Distribution of the QML When θ 0 is at the Boundary
      3. 8.3 Significance of the GARCH Coefficients
      4. 8.4 Diagnostic Checking with Portmanteau Tests
      5. 8.5 Application: Is the GARCH(1,1) Model Overrepresented?
      6. 8.6 Proofs of the Main Results
      7. 8.7 Bibliographical Notes
      8. 8.8 Exercises
    5. 9 Optimal Inference and Alternatives to the QMLE*
      1. 9.1 Maximum Likelihood Estimator
      2. 9.2 Maximum Likelihood Estimator with Mis‐specified Density
      3. 9.3 Alternative Estimation Methods
      4. 9.4 Bibliographical Notes
      5. 9.5 Exercises
  8. Part III: Extensions and Applications
    1. 10 Multivariate GARCH Processes
      1. 10.1 Multivariate Stationary Processes
      2. 10.2 Multivariate GARCH Models
      3. 10.3 Stationarity
      4. 10.4 QML Estimation of General MGARCH
      5. 10.5 Estimation of the CCC Model
      6. 10.6 Looking for Numerically Feasible Estimation Methods
      7. 10.7 Proofs of the Asymptotic Results
      8. 10.8 Bibliographical Notes
      9. 10.9 Exercises
    2. 11 Financial Applications
      1. 11.1 Relation Between GARCH and Continuous‐Time Models
      2. 11.2 Option Pricing
      3. 11.3 Value at Risk and Other Risk Measures
      4. 11.4 Bibliographical Notes
      5. 11.5 Exercises
    3. 12 Parameter‐Driven Volatility Models
      1. 12.1 Stochastic Volatility Models
      2. 12.2 Markov Switching Volatility Models
      3. 12.3 Bibliographical Notes
      4. 12.4 Exercises
  9. Appendix B: Ergodicity, Martingales, Mixing
    1. A.1. Ergodicity
    2. A.2. Martingale Increments
    3. A.3 Mixing
  10. Appendix B: Autocorrelation and Partial Autocorrelation
    1. B.1. Partial Autocorrelation
    2. B.2. Generalised Bartlett Formula for Non‐linear Processes
  11. Appendix C: Markov Chains on Countable State Spaces
    1. C.1. Definition of a Markov Chain
    2. C.2. Transition Probabilities
    3. C.3. Classification of States
    4. C.4. Invariant Probability and Stationarity
    5. C.5. Ergodic Results
    6. C.6. Limit Distributions
    7. C.7. Examples
  12. Appendix D: The Kalman Filter
    1. D.1. General Form of the Kalman Filter
    2. D.2. Prediction and Smoothing with the Kalman Filter
    3. D.3. Kalman Filter in the Stationary Case
    4. D.4. Statistical Inference with the Kalman Filter
  13. Appendix E: Solutions to the Exercises
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
  14. References
  15. Index
  16. End User License Agreement

Product information

  • Title: GARCH Models, 2nd Edition
  • Author(s): Christian Francq, Jean-Michel Zakoian
  • Release date: June 2019
  • Publisher(s): Wiley
  • ISBN: 9781119313571