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Stochastic Limit Theory: An Introduction for Econometricians (Advanced Texts in Econometrics), by James Davidson
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This is a survey of the recent developments in the rapidly expanding field of asymptotic distribution theory, with a special emphasis on the problems of time dependence and heterogeneity.
The book is designed to be useful on two levels. First as a textbook and reference work, giving definitions of the relevant mathematical concepts, statements, and proofs of the important results from the probability literature, and numerous examples; and second, as an account of recent work in the field of particular interest to econometricians, including a number of important new results. It is virtually self-contained, with all but the most basic technical prerequisites being explained in
their context; mathematical topics include measure theory, integration, metric spaces, and topology, with applications to random variables, and an extended treatment of conditional probability. Other subjects treated include: stochastic processes, mixing processes, martingales, mixingales, and
near-epoch dependence; the weak and strong laws of large numbers; weak convergence; and central limit theorems for nonstationary and dependent processes. The functional central limit theorem and its ramifications are covered in detail, including an account of the theoretical underpinnings (the weak convergence of measures on metric spaces), Brownian motion, the multivariate invariance principle, and convergence to stochastic integrals. This material is of special relevance to the theory of
cointegration.
- Sales Rank: #1907458 in eBooks
- Published on: 1994-10-13
- Released on: 1994-10-13
- Format: Kindle eBook
Review
"An excellent text."--W.G. Park, Assistant Professor of Economics, American University
"The chapters on the law of large numbers are superb. This book lays the foundation for serious econometrics. I wish I had spent a year studying it before graduate school. Well done!"--Henry Thompson, Auburn University
About the Author
James Davidson is at University of Wales, Aberystwyth.
Most helpful customer reviews
1 of 1 people found the following review helpful.
Fantastic introductdory reference book
By G. Calhoun
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.
12 of 12 people found the following review helpful.
Get ready for a hard time
By C. Hanck
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.)
0 of 0 people found the following review helpful.
One-stop reading for theoretical econometricians
By Kairat Mynbayev
I worked on various theoretical problems in econometrics. When I needed some theory, most of the time Davidson's book had it. Books in probabilities and statistics have too much material and examples that econometricians don't need (for example, I read Feller, Doob, and Rao). Davidson is good not only as a reference. It develops skills necessary for econometric research. It is a must for those PhD schools that claim to be centers of excellence.
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