The paper introduces a new nonparametric specification test for dynamic regression models. The test combines chi-square statistics based on Fourier series regression. A data-driven choice of the regression order, which uses the square root of the number of Fourier coefficients, is proposed. The benefits of the new test are (1) the selection procedure produces explicit and chi-square critical values that give a finite-sample size close to the nominal size; (2) the test is adaptive rate-optimal and detects local alternatives converging to the null with a rate that can be made arbitrarily close to the parametric rate. Simulation experiments illustrate the practical relevance of the new test.The first author acknowledges financial support from the Fonds Québécois de la Recherche sur la Société et la Culture (FQRSC). The second author acknowledges financial support from LSTA.

This paper proposes a bootstrap test for the correct specification of parametric conditional distributions. It extends Zheng's test (Zheng, 2000, Econometric Theory 16, 667–691) to allow for discrete dependent variables and for mixed discrete and continuous conditional variables. We establish the asymptotic null distribution of the test statistic with data-driven stochastic smoothing parameters. By smoothing both the discrete and continuous variables via the method of cross-validation, our test has the advantage of automatically removing irrelevant variables from the estimate of the conditional density function and, as a consequence, enjoys substantial power gains in finite samples, as confirmed by our simulation results. The simulation results also reveal that the bootstrap test successfully overcomes the size distortion problem associated with Zheng's test.We are grateful for the insightful comments from three referees and a co-editor that greatly improved the paper. Li's research is partially supported by the Private Enterprise Research Center, Texas A&M University. Fan is grateful to the National Science Foundation for research support.

This paper proposes a consistent nonparametric test for testing for equality of unknown conditional quantile curves across subgroups within a survey data framework. Moreover, to improve the small-sample performance of the test, we propose a modified version of wild bootstrap procedure in a quantile context. Monte Carlo evidence shows that the performance of the test in small samples is adequate but is improved significantly when the bootstrap critical values are used.I thank the co-editor and two referees for helpful comments that improved the paper. Financial support from the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged.

A new one-sided test for serial correlation in multivariate time series models is proposed. The test is based on a comparison between a multivariate spectral density estimator and the spectral density under the null hypothesis of no serial correlation. Duchesne and Roy (2004, Journal of Multivariate Analysis 89, 148–180) considered a multivariate kernel-based spectral density estimator. However, when the spectral density exhibits irregular features (because of strong autocorrelation or seasonality, among other factors), it is expected that a multivariate wavelet-based spectral density estimator will capture more effectively the local behavior of the spectral density. We consider a test based on a wavelet spectral density estimator, which represents a generalization of a test proposed by Lee and Hong (2001, Econometric Theory 17, 386–423). The asymptotic distribution of the new test is established under the null hypothesis, which is N(0,1). We propose and justify a suitable data-driven method to choose the smoothing parameter of the wavelet estimator (called the finest scale in that context). The new test should be powerful when the spectral density contains peaks or bumps. This is confirmed in a simulation study, where kernel-based and wavelet-based estimators are compared.The author thanks the co-editor Pentti Saikkonen and two referees for their constructive remarks and suggestions. Many thoughtful comments of the referees led to significant improvements of the paper. This work was supported by grants from the National Science and Engineering Research Council of Canada and the Fonds québécois de la recherche sur la nature et les technologies du Québec (Canada).

In this paper we provide an asymptotic analysis of generalized bipower measures of the variation of price processes in financial economics. These measures encompass the usual quadratic variation, power variation, and bipower variations that have been highlighted in recent years in financial econometrics. The analysis is carried out under some rather general Brownian semimartingale assumptions, which allow for standard leverage effects.Ole E. Barndorff-Nielsen's work is supported by the Centre for Analytical Finance (CAF), which is funded by the Danish Social Science Research Council. Neil Shephard's research is supported by the UK's ESRC through the grant “High frequency financial econometrics based upon power variation.” We thank the editor, Peter Phillips, and the referees for their stimulating comments on an earlier version.

This paper studies a semiparametric nonstationary binary choice model. Imposing a spherical normalization constraint on the parameter for identification purposes, we find that the maximum score estimator and smoothed maximum score estimator are at least [square root of n]-consistent. Comparing this rate to the convergence rate of the parametric maximum likelihood estimator (MLE), we show that when a normalization restriction is imposed on the parameter, the Park and Phillips (2000, Econometrica 68, 1249–1280) parametric MLE converges at a rate of n3/4 and its limiting distribution is a mixed normal. Finally, we show briefly how to apply our estimation method to a nonstationary single-index model.The first draft of the paper was written while Guerre was visiting the economics department of the University of Southern California. We thank Peter C.B. Phillips, a co-editor, and three anonymous referees for helpful comments and John Dolfin for proofreading. Guerre thanks the economics department of the University of Southern California for its hospitality during his visit. Moon appreciates financial support of the University of Southern California faculty development award.

This note uses fixed bandwidth (fixed-b) asymptotic theory to suggest a new approach to testing cointegration parameters in a single-equation cointegration environment. It is shown that the standard tests still have asymptotic distributions that are free of serial correlation nuisance parameters regardless of the bandwidth or kernel used, even if the regressors in the cointegration relationship are endogenous.I thank Tim Vogelsang for his guidance, Pentti Saikkonen for the promptness with which he provided me with an old working paper of his, Wayne Fuller for several discussions, and an anonymous referee for many helpful comments. The usual disclaimer applies.

In this note the nonparametric unit root test of Burridge and Guerre (1996, Econometric Theory, 12, 705–723), which is based on the standardized number of crossings of a level of a random walk, is extended in two ways, allowing for a deterministic trend in the process and more general innovations. The test has a well-known standard limit distribution. Monte Carlo experiments revealed the good finite-sample properties of the proposed test.The authors appreciate helpful comments from an anonymous referee. We gratefully acknowledge the financial support of the Ministerio de Ciencia y Tecnología and the Conselleria d'Economia, Hisenda i Innovació, grants BEC2002-03769 and PRIB-2004-10095, respectively.

Econometric Theory is proud to announce the winning article for The Tjalling C. Koopmans Econometric Theory Prize for the period 2003–2005 inclusive.