TJALLING C. KOOPMANS PRIZES
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
Yongmiao Hong and Tae-Hwy Lee, "Diagnostic
Checking for the Adequacy of Nonlinear Time Series Models," Econometric Theory,
Vol. 19, No. 6, December 2003, pages 10651121.
This paper proposes a diagnostic test for the adequacy of time series models, allowing
for rather general model classes, involving possibly nonlinear parametric functions of
past information that include both conditional heterogeneity and conditional duration
specifications. The test is based on the estimated noise process, relying on the joint and
marginal characteristic functions of pairs of noise variables at different time distances
to test for pairwise independence. The test employs the (generalized) spectrum of these
quantities and therefore does not require moment conditions, and applies under a suitable
mixing condition. Under the null of correct specification the generalized spectrum is
constant and the test measures departures from this null using a standardized L2
distance. Asymptotic properties of the test are derived, data driven choices of the
bandwidth for estimation of the generalized spectrum and their asymptotic properties are
discussed, Monte Carlo studies are presented and an empirical application to daily stock
prices is given.
Stefan Sperlich, Dag Tjøstheim and Lijian Yang,
"Nonparametric Estimation and Testing of Interaction in Additive Models," Econometric
Theory, Vol. 18, No. 2, April 2002, pp 197251.
The article was selected by the journals Advisory Board from papers published in Econometric
Theory over the period 2000-2002 inclusive. The citation accompanying the award is as
A large and useful class of nonlinear models, obtained by generalizing additive models
through adding second order interaction terms, is analyzed using nonparametric techniques.
This is a wide-open area for research and it is very useful to have available a firm
foundation for empirical research in the area. The authors develop asymptotics for
marginal integration and backfitting estimation techniques. They propose procedures for
testing interaction effects and suggest bootstrap methods. Finally, they provide
simulation evidence and give an empirical implementation to a livestock production
Stéphane Gregoir, "Multivariate Time Series with Various Hidden
Unit Roots, Part I: Integral Operator Algebra and Representation," Econometric
Theory, Vol. 15, 1999, pp. 435468.
Stéphane Gregoir is awarded the Tjalling Koopmans Econometric Theory Prize
for a pair of related high quality papers. The first considers a vector of time series,
each of which may contain several unit roots of various frequencies. There may also exist
several linear combinations, or generalized cointegrations, which produce series with less
unit roots. A general representation theorem is stated, with an associated vector error
correction model. The theory includes as special cases the standard cointegration model
with I(1) series, multi-cointegration with I(2) series and seasonal unit root
cointegration. This representation theorem is a substantial and useful addition to the
The second paper develops estimation and test strategies for models with possible multiple
unit roots at the zero and seasonal frequencies, together with polynomial (in lags)
error-correction terms, possibly with deterministic terms. Although the situation
considered is rather complicated the empirical techniques use simple procedures such as
Richard A. Davis and William T.M. Dunsmuir,
"Maximum Likelihood Estimation for MA(1) Processes With A Root on or Near the Unit
Circle," Econometric Theory, Vol. 12, 1996, pp. 129.
The paper solves one of the last open questions in the asymptotic theory of likelihood
estimation for ARMA models, concerning the properties of estimates of parameter estimates
for MA(1) models on and near the unit circle. The results are both of theoretical and of
practical interest, as it is found, for example, that estimates are surprisingly accurate
even for small sample sizes.
Because of the quality of the theoretical analysis, of the importance of the question
considered, and of the practical relevance of the results, it is thought that this paper
deserves the Koopmans Prize.
Pentti Saikkonen, "Estimation of Cointegration Vectors with Linear
Restrictions," Econometric Theory, Vol. 9, 1993, pp 1935.
This paper develops a general method of estimating and testing cointegration vectors
with linear restrictions. In the case of zero restrictions the cointegration relations are
formally similar to the structural equations of a traditional simultaneous equations
model, and the paper provides an important link between the literature on statistical
inference in simultaneous equations models and the more recent literature on cointegration
analysis. The asymptotic distribution of the estimators are shown to be mixed normal, so
that Wald tests with asymptotic chi-square distributions under the null hypothesis are
obtained in the usual way. Convenient test procedures for checking the validity of
overidentifying restrictions are also provided.
Katsuto Tanaka, "An Alternative Approach to the Asymptotic Theory of
Spurious Regression, Cointegration, and Near Cointegration," Econometric Theory,
Vol. 9, 1993, pp 3661.
This paper uses the Fredholm approach in order to derive new expressions for the
asymptotic sampling distributions of estimators and test statistics in cointegration
models. It is shown that, in some cases, these expressions provide a basis for the
accurate computation of the limiting distributions. The paper also introduces a definition
of near cointegration, for which asymptotic properties are studied. It then devises tests
which take cointegration as the null hypothesis and discusses the limiting local power of
these tests under the alternative of near cointegration.
Yuzo Hosoya, Yoshihiko Tsukuda and Nobuhiko Terui, "Ancillarity and the
Limited Information Maximum-Likelihood Estimation of a Structural Equation in a
Simultaneous Equation System," Econometric Theory, Vol. 5, 1989, pp
In this paper three concepts in current research are focused on the now classical
econometric methodology of limited information maximum likelihood estimation in
simultaneous equation models. The model under the assumption of normality constitutes a
curved exponential family of distributions. The effect of conditioning on the ancillary
statistic of the smallest root of the usual determinantal equation is analyzed by means of
second-order asymptotics. This study gives new insight into a familiar subject and
suggests promising approaches to other econometric problems.
Christian Gourieroux, Alan Monfort and Alain Trognon, "A General Approach
to Serial Correlation," Econometric Theory, Vol. 1, 1985, pp 315340.
This paper is a fundamental contribution to econometric theory. It provides a general
framework for analyzing systematically a variety of autoregressive models with latent
variables, including nonlinear simultaneous equation models, qualitative response models,
and disequilibrium models. The authors show how diverse testing and estimation problems
can be handled by this approach. It can be expected that this paper, which organizes the
statistical analysis of data with time dependence, will also stimulate the development of