Customer Reviews

Stochastic Limit Theory: An Introduction for Econometricicans (Advanced Texts in Econometrics)

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Yes, I know it's a standard game of reviewers to show off by describing books as "a good introduction", implying one's capability of easily absorbing the material.

I shall try to judge the book by its stated mission, viz. to be an "introduction for econometricians". In my view it isn't, the material doesn't resemble much of what you are likely to have encountered in your econometrics education. If anything it is a course in applied measure theory. I should add that I don't know how the original sources look like (e.g. Billingsley), perhaps they're even worse. I just don't see where the book is supposed to be tailored to the background and needs of econometricians (with the exception of convergence to stochastic integrals at the very end, relevant for unit root econometrics etc.). Motivation and relevant examples (e.g. links to econometrics which one might reasonably expect in view of the title) are scarce, or to put it in Davidson's words, they occur on a set with measure zero. The book is thus extremely terse. It's Theorem - Proof - Corollary at its best. The back cover even recommends the book to business econometricians also (whatever that may be). This must be a marketing gag by the publisher, as far as I can judge the business world.

On the other hand it is quite self contained, which means most concepts you need in the later parts of the book are developed (if briefly) in the introductory chapters. Davidson frequently helps you with the task of understanding the proofs (which cover an estimated 2/3 of the book) by referring you to the relevant places.

It is only fair to acknowledge that Davidson does a remarkable job of explaining the material rigorously, but just don't be fooled by the title. It's hard work, you have to spend time on each word and (there is a lot more of that obviously) (in)equality.

Happily, it's worth it. Once you're through this, some of these obscure appendices in Econometrica may at last become more accessible to you. (The converse also holds: if you have never been interested in the details of the proofs save your money.)

As another reviewer noted, there are absolutely no "real world" examples in this book. But that's not really the point. This book covers many of the theorems and techniques you would need to prove asymptotic results for time series, and I refer to it almost daily. The book would be extremely difficult for someone who hasn't taken a graduate sequence in econometrics or had similar mathematical preparation.

It's the first book I look at when I want to understand the details of a concept (mixing, for example), and I wish that Davidson had included some more topics that are related to my current research... that combination should make this an ideal introductory book, even though the material is inherently difficult.

This is a very good book on stochastics as it covers a lot of advanced topics in detail. I particularly found helpful the coverage of weak convergence. If you want to master the realm of stochastic processes, this could be a great place to start.