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I recently graduated as an undergraduate statistics major with a bit of a dense math background (I know some probability theory and stochastic calculus and took two semesters of real analysis and abstract algebra). I'm a bit disappointed, since despite all of the theory I have learned, I don't have too much background in terms of applying what I've learned.

The only experience I have with applications is an introductory-level econometrics course, which strangely enough was not required for the statistics major (I took it back when I was still an actuarial major). I found that class to be a bore with the lack of mathematical rigor in it, and I asked the professor for a proof of the Gauss-Markov Theorem while I took the course.

For someone with my mathematical background, what would you recommend as mathematically-oriented textbooks for learning about econometrics and issues that come with creating models (multicollinearity, heteroskedasticity, serial correlation, etc.)?

(If my question is vaguely worded, let me know, and I can edit it to be more specific.)

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It would help if you clarify what sort of models you are interested in: macro vs micro, time series, panel or cross section, demand estimation, or casual inference, etc.. I am afraid there's not one book that covers them all well. –  Dimitriy V. Masterov May 30 at 7:27
Made the question more specific. Thanks! –  Clarinetist May 30 at 7:31
It may not be quite as mathematical as you want, but I highly recommend Harrell's Regression Modeling Strategies. –  Glen_b May 31 at 7:42

6 Answers 6

up vote 2 down vote accepted

With your background I would look to " The Elements of Statistical Learning " (Springer) by Hastie, Trevor, Tibshirani, Robert, Friedman, Jerome.

Another good book is A. C. Davison: "Statistical Models" (Cambridge)

But, the one book you REALY, REALLY should study is this one: David A. Freedman: "Statistical Models. Theory and Practice. Revised Edition." (Cambridge) From the foreword by some friends: "Some books are correct. Some are clear. Some are useful. Some are entertaining. Few are even two of these. This book is all four. Statistical Models: Theory and Practice is lucid, candid and insightful, a joy to read. We are fortunate that David Freedman finished this new edition before his death in late 2008. We are deeply saddened by his passing, and we greatly admire the energy and cheer he brought to this volume—and many other projects—during his final months. "

This book is low on mathematics (which does NOT mean "easy"), but high on the conceptual side, and not only presents models, but critizes them too. You will love it!

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By the way, I checked out Freedman. It is a joy to read, and is sufficiently mathematical for my purposes. Thank you for telling me about it. –  Clarinetist 1 hour ago

If you want a mixture of application and rigor, I would recommend the two Wooldridge books. One book is a graduate-level text, and the other is aimed at undergraduate students. I would try the first one given your background. There are proofs, but there are also empirical examples, with the datasets readily available. The focus is mainly on cross sectional and panel data topics, though everything you mention is covered.

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If you are looking for Time Series in finance, here is a great book :

Tsay, R. S. (2010) Analysis of Financial Time Series. Third Edition. New York: Wiley.

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May I add the two Brockwell and Davis books? –  Sergio May 30 at 7:50

I just finished a data mining class at University and we used "Data Mining for Business Intelligence Concepts, Techniques, and Applications in Microsoft Office Excel With Xlminer" By Shmueli, Patel, and Bruce. The professor also had readings in the Hastie, Tbshirani, and Friedman which can be found here . These gave a pretty good introduction and it was a pretty mathematically rigorous class.

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If you're interested in learning about different econometric methodologies (how to go about creating models and dealing with issues encountered) then I'd recommend the following books:

  • Modelling Economic Series: Readings in Econometric Methodology (Advanced Texts in Econometrics) by C. W. J. Granger.
  • Modelling Nonlinear Economic Time Series (Advanced Texts in Econometrics) by Timo Terasvirta, Dag Tjostheim, Clive W. J. Granger.
  • Dynamic Econometrics (Advanced Texts in Econometrics) by David F. Hendry.
  • Statistical Foundations of Econometric Modelling by Aris Spanos.
  • Specification Searches: Ad Hoc Inference with Nonexperimental Data by Edward E. Leamer.
  • Forecasting, Structural Time Series Models and the Kalman Filter by Andrew C. Harvey.

For a history of the evolution of econometrics, see:

  • The Foundations of Econometric Analysis (Econometric Society Monographs) by David F. Hendry, Mary S. Morgan.

There's a good deal of math and notation to get through in these books. (Unfortunately, a unified notation is not really used in the field.)

I'd suggest starting with the first book on the list, which is a collection of papers, because it will give an introduction and overview of issues in econometric methodology. Indeed, it will help put the material in the other books into context and makes things more digestible.

If you'd like a shorter read, you can get a taste of the econometric methodology literature by checking out a recent article by Ray C Fair: Reflections on Macroeconometric Modeling

For more recommendations, check out the references listed in each of the aforementioned books. There's tonnes of (exciting) stuff for you to get your teeth through.

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I liked the book "The practise of Business Statistics" as a good verbose introduction to the application of creating models with some real world data with real world problems. The mathematics in the book is probably elementary for your calibre/background, but I would still recommend it. Here is good list of books which deal with the application of modelling to more real world problems and applications. HTH

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