The Tjalling C. Koopmans Econometric Theory Prize is
named in honor of Tjalling C. Koopmans, the 1975 Nobel Laureate in economic science, whose
contributions to the development of econometrics are of fundamental and lasting importance
to the subject. The prize is awarded once every three years for the best article reporting
original research published in the Journal Econometric Theory over that
period. The selection of the winning article is made by the Advisory
Board of the Journal and the criteria for selection is based on Tjalling
Koopmans own research which is universally admired for its rigor, clarity and
originality. All articles published in Econometric Theory are candidates
for the prize except those that are authored or co-authored by the Editor and members of
the Advisory Board.
The prize is accompanied by a financial award of $1,000. It is supported by the
publishers, Cambridge University Press, and Mrs. Truus Koopmans.
Cambridge University Press joins me in congratulating the authors on their success in
receiving this award.
Wei Biao Wu and Xiaofeng Shao, "A
Limit Theorem for Quadratic Forms and its Applications," Econometric Theory,
Vol. 23, No. 5, October 2007, pages 930-951.
The paper derives a central limit theorem for quadratic
forms of martingale differences. Particular emphasis is laid on the
application of this result to estimation of the spectral density of a
stationary process by the smoothed periodogram. For this case
asymptotic normality is obtained from the result on general quadratic
forms by approximating the Fourier transforms of the underlying
stationary process by martingales. Such limiting results are
important, for instance for hypothesis testing and construction of
confidence intervals in frequency domain.
For both, the general case and for the special
case of estimation of spectra, there exists a substantial body of
preceding literature. A special feature of this paper is that the
results are derived under assumptions which are very general and
easily verifiable. For spectral estimation the main assumptions are
that the underlying stationary process is obtained from a – in general
non-linear – causal transformation of an i.i.d. sequence and a very
weak assumption of short range dependence. By the first
assumption the stationary process can be interpreted as the output of
a general, possibly nonlinear, system with iid inputs. The class of
such processes is very large. The second assumption avoids the
classical strong mixing conditions or summability conditions on the