This edition contains a large number of additions and corrections. The analysis of GARCH models – and more generally volatility models – has undergone various new developments in recent years. There was a need to make the material more complete.

A brief summary of the added material in the second edition is:

1. A new chapter entitled “Parameter‐driven volatility models”. This chapter is divided in two sections entitled “Stochastic Volatility Models” and “Markov Switching Volatility Models”. Two new appendices on “Markov Chains on Countable State Spaces” and “The Kalman Filter” are provided.
2. A new chapter entitled “Alternative Models for the Conditional Variance”, replacing and completing the chapter “Asymmetries” of the first version. This chapter contains a new section on “Stochastic Recurrence Equations” and additional material on EGARCH, Log‐GARCH, GAS, MIDAS and intraday volatility models among others.
3. A more complete discussion of multivariate GARCH models in Chapter 10. In particular a new section on “Cholesky GARCH” has been added. More emphasis has been given to the inference of multivariate GARCH models, through two new sections entitled “QML Estimation of General MGARCH” and “Looking for Numerically Feasible Estimation Methods”.
4. The previous Appendix D entitled “Problems” has been removed, but a new set of corrected problems is available on the webpages of the authors.
5. An up‐to‐date list of references.

On the other hand, there was not enough space to keep the previous 4th chapter of the 1st edition entitled “Temporal aggregation and weak GARCH models”.

The webpage http://christian.francq140.free.fr/Christian-Francq/book-GARCH.html features additional material (codes, data sets, and problems with corrections)

We are indebted to many readers who have used the book and made suggestions for improvements. In particular, we thank Francisco Blasques, Lajos Horvàth, Hamdi Raïssi, Roch Roy, Genaro Sucarrat. We are also indebted to Wiley for their support and assistance in preparing this edition.

Palaiseau, France

September, 2018