ARCH-model

R.F. Engle invented the ARCH model (1982). Since then, such models (the original ARCH and a plethora of cousins inspired by Engle's.) appear every time you deal with heteroscedasticity problems. Being one of the most important developments of the last 20 years, every manual dealing with that is welcome. As the title suggests, this one is a collection of the most important papers of the ARCH literature. You'll find among others, the original Engle's paper presenting the ARCH, Bollerslev paper proposing the GARCH, Engle, Lilien and Robins ARCH-M paper, and many others dealing with their stationarity, the advantages of being good diffusion approximations, many empirical studies (stock returns and its volatility, exchange rates, etc...) and semi-parametric ARCH models. I can't deny the utility of the manual (If you are able to read the whole book, you'll understand pretty well the ARCH theory), but be warned, you won't have the very latest developments, the ones that appeared during the 90 decade (I recommend, in that case, to buy "Non-Linear time series models in empirical finance", by Franses and van Dijk). All the articles here appeared in specialized econometric journals; Robert Engle chooses the most important ones. This book is good, but you should be aware that some of the articles are particularly difficult as the ones written by Nelson, a brilliant econometrician. I think undergraduate students won't appreciate the book, it's pretty hard; even graduate students not specialized in econometrics will have problems. It's a book for those knowing already something about ARCH, the others, if they want to learn, should start somewhere else. I propose James D. Hamilton book or, a simpler one, Enders manual.

This text is not helpful to the reader who wishes to devise and estimate GARCH models. Moreover it provides no insight into the practical use of these models in the analyses of financial data. Much of the material appears to be lecture notes by an academic who has no idea of how to apply GARCH models. Particularly missing is any discussion of how to estimate the parameters of GARCH models.

So far, I own three books of Gourieroux. This one is the first I enjoyed reading. ARCH-type models are pretty recent (Engle, 1982) and I think there is not a plethora of manuals dealing with them at an introductory level. This is not exactly an introductory book; but it covers extensively (till 1993) the topic and gives all the statistical results and demonstrations. The first chapters are particularly good: the introduction is pretty clear and persuasive; the explanation of stationarity proves to be very useful and the examples of no linearity resume well the mathematical tools available nowadays. After that, the challenging part begins: a chapter introducing the ARCH model (all statistical properties appear there), another one dealing with estimation and test procedures, GARCH... Half of the manual is dedicated to interesting (but sometimes pretty complex) financial applications, such as the CAPM model. It has to be said that you require a very solid mathematical knowledge (not for undergraduate economists); otherwise, you will feel frustrated. I personally recommend (for those ignoring everything about ARCH's) to get started with Johnston and Dinardo's brief chapter of ARCH (Econometric Methods), then reading the very same chapter in Ender's manual and then reading Hamilton's ARCH's chapter. Once you understood this literature, you will be able to read comfortably Gourieroux's manual, which is far more complete than the others. There is a lot of mathematical formulation, but this time, Gourieroux explains it better than usual.

Gourieroux is an expert in econometrics and has written several excellent texts on time series analysis and its application in economics and finance in particular. This text specializes as a primer on ARCH models. These models are very useful in finance where the time series are often nonlinear and volatile. This text covers the subject in just over 200 pages. Many useful references are provided in the various reference lists at teh back of the book.