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Advanced Texts in Econometrics
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Recent years have seen a marked increase in the mathematical sophistication of econometric research. While the theory of linear parametric models which forms the backbone of the subject makes an extensive and clever use of matrix algebra, the statistical prerequisites of this theory are comparatively simple. But now that these models are pretty thoroughly understood, research is concentrated increasingly on the less tractable questions, such as nonlinear and nonparametric estimation and nonstationary data generation processes. The standard econometrics texts are no longer an adequate guide to this new technical literature, and a sound understanding of the probabilistic foundations of the subject is becoming less and less of a luxury.
The asymptotic theory traditionally taught to students of econometrics is founded on a small body of classical limit theorems, such as Khinchine's weak law of large numbers and the Lindeberg-Lévy central limit theorem, relevant to the stationary and independent data case. To deal with linear stochastic difference equations, appeal can be made to the results of Mann and Wald (1943a), but even these are rooted in the assumption of independent and identically distributed disturbances. This foundation has become increasingly inadequate to sustain the expanding edifice of econometric inference techniques, and recent years have seen a systematic attempt to construct a less restrictive limit theory. Hall and Heyde's Martingale Limit Theory and its Application (1980) is an important landmark, as are a series of papers by econometricians including among others Halbert White, Ronald Gallant, Donald Andrews, and Herman Bierens. This work introduced to the econometrics profession pioneering research into limit theory under dependence, done in the preceding decades by probabilists such as J. L. Doob, I. A. Ibragimov, Patrick Billingsley, Robert Serfling, Murray Rosenblatt, and Donald McLeish
C.W.J.Granger & G.E.Mizon - Personal Name
1st Edtion
0-19-877402-8
NONE
Advanced Texts in Econometrics
Economics
English
Oxford University Press Inc.
1994
USA
1-562
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