The exact discrete model satisfied by equispaced data generated by a linear stochastic differential equations system is derived by a method that does not imply restrictions on observed discrete data per se. The method involves integrating the solution of the continuous time model in state space form and a nonstandard change in the order of three types of integration, facilitating the representation of the exact discrete model as an asymptotically time-invariant vector autoregressive moving average model. The method applying to the state space form is general and is illustrated using the prototypical higher order model for mixed stock and flow data discussed by Bergstrom (1986, Econometric Theory 2, 350–373).

Semiparametric and nonparametric estimation have attracted a great deal of attention from statisticians and theoretical econometricians in the past decade. Various new models have been proposed, and new methods for estimating those models have been suggested. These new models and methods are scattered in various academic journals and are not easily accessible to other researchers. Moreover, the new methods are technical, not easily understood by nonexperts such as graduate students and applied econometricians. Horowitz has two goals in his book Semiparametric Methods in Econometrics. First, he wants to provide a central place for those who want to check out the semiparametric literature. Second, he wants to present technical materials in a nontechnical way so that graduate students and applied econometricians who often do not have expertise in this area can comprehend the new methods. In my view, Horowitz has achieved both goals.

The accessibility of high-performance computing power has always influenced theoretical and applied econometrics. Gouriéroux and Monfort begin their recent offering, Simulation-Based Econometric Methods, with a stylized three-stage classification of the history of statistical econometrics. In the first stage, lasting through the 1960's, models and estimation methods were designed to produce closed-form expressions for the estimators. This spurred thorough investigation of the standard linear model, linear simultaneous equations with the associated instrumental variable techniques, and maximum likelihood estimation within the exponential family. During the 1970's and 1980's the development of powerful numerical optimization routines led to the exploration of procedures without closed-form solutions for the estimators. During this period the general theory of nonlinear statistical inference was developed, and nonlinear micro models such as limited dependent variable models and nonlinear time series models, e.g., ARCH, were explored. The associated estimation principles included maximum likelihood (beyond the exponential family), pseudo-maximum likelihood, nonlinear least squares, and generalized method of moments. Finally, the third stage considers problems without a tractable analytic criterion function. Such problems almost invariably arise from the need to evaluate high-dimensional integrals. The idea is to circumvent the associated numerical problems by a simulation-based approach. The main requirement is therefore that the model may be simulated given the parameters and the exogenous variables. The approach delivers simulated counterparts to standard estimation procedures and has inspired the development of entirely new procedures based on the principle of indirect inference.

We point out the close relationship between the integrated conditional moment tests in Bierens (1982, Journal of Econometrics 20, 105–134) and Bierens and Ploberger (1997, Econometrica 65, 1129–1152) with the complex-valued exponential weight function and the kernel-based tests in Härdle and Mammen (1993, Annals of Statistics 21, 1926–1947), Li and Wang (1998, Journal of Econometrics 87, 145–165), and Zheng (1996, Journal of Econometrics 75, 263–289). It is well established that the integrated conditional moment tests of Bierens (1982) and Bierens and Ploberger (1997) are more powerful than kernel-based nonparametric tests against Pitman local alternatives. In this paper we analyze the power properties of the kernel-based tests and the integrated conditional moment tests for a sequence of “singular” local alternatives, and show that the kernel-based tests can be more powerful than the integrated conditional moment tests for these “singular” local alternatives. These results suggest that integrated conditional moment tests and kernel-based tests should be viewed as complements to each other. Results from a simulation study are in agreement with the theoretical results.

Karanasos (1998) presented a new method for computing the theoretical autocovariance function (acf) of the following univariate autoregressive moving average (ARMA) model:

Φ(L)yt = Θ(L)εt

where

Φ(L) = 1 − φ1L − … − φpLp, Θ(L) = 1 − θ1L − … − θqLq

The inaugural meeting of the NZESG was held in February 1997 and comprised 14 papers, a software demonstration, and a roundtable panel discussion. Around 15 participants attended throughout, with stronger attendance on the first day.

The fourth edition of Econometric Methods by Jack Johnston and John DiNardo, is a rewrite of the venerable third edition by Johnston that sustained several generations of economists. As stated by the authors themselves, the reason for undertaking this major revision is to provide a comprehensive and accessible account of currently available econometric methodology, and in my opinion they have been successful in achieving their objective. The book has 13 chapters and runs to 531 pages. Each chapter ends with a selection of problems, several of which are new to this edition. Answers are not provided, although a solutions manual is available. Two appendices, one on matrix algebra and the other on statistical preliminaries, are intended to make the book as self-contained as possible. Not unexpectedly, the appendices are somewhat tersely worded, and the reader may wish to supplement them with additional reference material. Conforming to current practice, the book is accompanied by a data diskette containing several data sets, allowing the reader to replicate the applications given in the text.