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

Rating:
Summary: complete, excellent
Review: This is an excellent book on stochastic convergence. The book is oriented toward advanced graduate students in economics and researchers that have to use econometrics in practice, and its main aim is to introduce this audience to advanced mathematical concepts that are needed in order to deal with stochastic convergence. The first part of this book (about 200 pages) is preliminaries from real analysis, measure and probability theory. Then it discusses theory of stochastic processes, introducing among others such concepts as martingales and mixingales, and then it moves to the main part - various limit results (about 300 pages). It discusses in great detail Laws of Large Numbers and Central Limit Theorems for various sequences of random variables: from simple iid cases to dependent non-identicali distributed. It concludes with the section on Functional Central Limit Theorems. This textbook is practically complete, it contains huge amount of material and almost all results are provided with proofs. It was recommended to as by prof. Phillips for his Time-Series Econometrics course ar Yale, but I find it very useful for other courses in statistics and finance too. It is just a great reference book and if you study econometrics at advanced level or you have to read modern econometrics literature you would appreciate it. It could be also a good idea to combine reading of this book with White's "Asymptotic Theory For Econometricians". The last one is very compact and it adapts results found in Davidson's book to the case of linear regression model.