A new consistent test is proposed for the parametric specification of the diffusion function in a diffusion process without any restrictions on the functional form of the drift function. The data are assumed to be sampled discretely in a time interval that can be fixed or lengthened to infinity. The test statistic is shown to follow an asymptotic normal distribution under the null hypothesis that the parametric diffusion function is correctly specified. Monte Carlo simulations are conducted to examine the finite-sample performance of the test, revealing that the test has good size and power.The author is grateful to Yacine Aït-Sahalia, John Knight, Oliver Linton (the co-editor), Greg Tkacz, Jun Yang, and three anonymous referees for helpful comments and suggestions. He also thanks seminar participants at the Bank of Canada, the 2004 Semiparametrics Conference in Rio de Janeiro, and the 2005 Econometric Study Group in Bristol. The views expressed in this paper are those of the author. No responsibility for them should be attributed to the Bank of Canada.

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.

Forecast accuracy is typically measured in terms of a given loss function. However, as a consequence of the use of misspecified models in multiple model comparisons, relative forecast rankings are loss function dependent. In order to address this issue, a novel criterion for forecast evaluation that utilizes the entire distribution of forecast errors is introduced. In particular, we introduce the concepts of general-loss (GL) forecast superiority and convex-loss (CL) forecast superiority; and we develop tests for GL (CL) superiority that are based on an out-of-sample generalization of the tests introduced by Linton, Maasoumi, and Whang (2005, Review of Economic Studies 72, 735–765). Our test statistics are characterized by nonstandard limiting distributions, under the null, necessitating the use of resampling procedures to obtain critical values. Additionally, the tests are consistent and have nontrivial local power, under a sequence of local alternatives. The above theory is developed for the stationary case, as well as for the case of heterogeneity that is induced by distributional change over time. Monte Carlo simulations suggest that the tests perform reasonably well in finite samples, and an application in which we examine exchange rate data indicates that our tests can help identify superior forecasting models, regardless of loss function.

The aim of this paper is the study of the path solutions of a multivariate rational expectations model. We describe several procedures for solving such dynamic systems based on either the adjoint operator method or the Smith form. As a by-product, we derive the dimension of the set of solutions in terms of martingale differences and the dimension of the set of linear stationary solutions when we restrict ourselves to the linear case. These dimensions are functions of the number of equations in the system, of the maximum lead, and of the orders of some eigenvalues of the characteristic equation associated with the system.

The Wald test for linear restrictions on cointegrating vectors is compared in finite samples using the Monte Carlo method. The Wald test is calculated within the vector error-correction based estimation methods of Bewley, Orden, Yang, and Fisher (1994, Journal of Econometrics 64, 3–27) and of Johansen (1991, Econometrica 59, 1551–1580), the canonical cointegration method of Park (1992, Econometrica 60, 119–143), the dynamic ordinary least squares method of Phillips and Loretan (1991, Review of Economic Studies 58, 407–436), Saikkonen (1991, Econometric Theory 7, 1–21), and Stock and Watson (1993, Econometrica 61, 783–820), the fully modified ordinary least squares method of Phillips and Hansen (1990, Review of Economic Studies 57, 99–125), and the band spectral techniques of Phillips (1991, in W. Barnett, J. Powell, & G. E. Tauchen (eds.), Nonparametric and Semiparametric Methods in Economics and Statistics, pp. 413–435). The Wald test performance is also compared to that of the likelihood ratio test suggested by Johansen and Juselius (1990, Oxford Bulletin of Economics and Statistics 52, 169–210) and to a Bartlett correction of that test as proposed by Johansen (1998, A Small Sample Test for Tests of Hypotheses on Cointegrating Vectors, European University Institute).

This paper studies the asymptotic properties of a nonstationary partially linear regression model. In particular, we allow for covariates to enter the unit root (or near unit root) model in a nonparametric fashion, so that our model is an extension of the semiparametric model analyzed in Robinson (1988, Econometrica 56, 931–954). It is proved that the autoregressive parameter can be estimated at rate N even though part of the model is estimated nonparametrically. Unit root tests based on the semiparametric estimate of the autoregressive parameter have a limiting distribution that is a mixture of a standard normal and the Dickey–Fuller distribution. A Monte Carlo experiment is conducted to evaluate the performance of the tests for various linear and nonlinear specifications.We thank Bruce Hansen, Roger Koenker, Helmut Lütkepohl, Peter Phillips, three referees, and participants of the 8th World Congress of the Econometric Society and the 10th Midwest Econometrics Group Meeting for helpful comments on an earlier version of this paper. This investigation was supported by the University of Kansas General Research Fund allocation 2301789-003.

We propose a test for a generalized regression monotonicity (GRM) hypothesis. The GRM hypothesis is the sharp testable implication of the monotonicity of certain latent structures, as we show in this article. Examples include the monotonicity of the conditional mean function when only interval data are available for the dependent variable and the monotone instrumental variable assumption of Manski and Pepper (2000). These instances of latent monotonicity can be tested using our test. Moreover, the GRM hypothesis includes regression monotonicity and stochastic monotonicity as special cases. Thus, our test also serves as an alternative to existing tests for those hypotheses. We show that our test controls the size uniformly over a broad set of data generating processes asymptotically, is consistent against fixed alternatives, and has nontrivial power against some ${n^{ - 1/2}}$ local alternatives.

Professor David F. Hendry is interviewed by Neil R. Ericsson.

Often neither the exact density nor the exact cumulative distribution function (c.d.f.) of a statistic of interest is available in the statistics and econometrics literature (e.g., the maximum likelihood estimator of the autocorrelation coefficient in a simple Gaussian AR(1) model with zero start-up value). In other cases the exact c.d.f. of a statistic of interest is very complicated despite the statistic being “simple” (e.g., the circular serial correlation coefficient, or a quadratic form of a vector uniformly distributed over the unit n-sphere). The first part of the paper tries to explain why this is the case by studying the analytic properties of the c.d.f. of a statistic under very general assumptions. Differential geometric considerations show that there can be points where the c.d.f. of a given statistic is not analytic, and such points do not depend on the parameters of the model but only on the properties of the statistic itself. The second part of the paper derives the exact c.d.f. of a ratio of quadratic forms in normal variables, and for the first time a closed form solution is found. These results are then specialized to the maximum likelihood estimator of the autoregressive parameter in a Gaussian AR(1) model with zero start-up value, which is shown to have precisely those properties highlighted in the first part of the paper.

An estimator of a finite-dimensional parameter is said to be doubly robust (DR) if it imposes parametric specifications on two unknown nuisance functions, but only requires that one of these two specifications is correct in order for the estimator to be consistent for the object of interest. In this article, we study versions of such estimators that use local polynomial smoothing for estimating the nuisance functions. We show that such semiparametric two-step (STS) versions of DR estimators have favorable theoretical and practical properties relative to other commonly used STS estimators. We also show that these gains are not generated by the DR property alone. Instead, it needs to be combined with an orthogonality condition on the estimation residuals from the nonparametric first stage, which we show to be satisfied in a wide range of models.

In this paper we extend the large-sample results provided for the augmented Dickey–Fuller test by Said and Dickey (1984, Biometrika 71, 599–607) and Chang and Park (2002, Econometric Reviews 21, 431–447) to the case of the augmented seasonal unit root tests of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), inter alia. Our analysis is performed under the same conditions on the innovations as in Chang and Park (2002), thereby allowing for general linear processes driven by (possibly conditionally heteroskedastic) martingale difference innovations. We show that the limiting null distributions of the t-statistics for unit roots at the zero and Nyquist frequencies and joint F-type statistics are pivotal, whereas those of the t-statistics at the harmonic seasonal frequencies depend on nuisance parameters that derive from the lag parameters characterizing the linear process. Moreover, the rates on the lag truncation required for these results to hold are shown to coincide with the corresponding rates given in Chang and Park (2002); in particular, an o(T1/2) rate is shown to be sufficient.

We introduce a kernel-based estimator of the density function and regression function for data that have been grouped into family totals. We allow for a common intrafamily component but require that observations from different families be independent. We establish consistency and asymptotic normality for our procedures. As usual, the rates of convergence can be very slow depending on the behavior of the characteristic function at infinity. We investigate the practical performance of our method in a simple Monte Carlo experiment.

This paper derives sufficient conditions for global identification in nonlinear models characterized by a finite number of unconditional moment restrictions. The main contribution of this paper is to provide a set of assumptions that are alternative to those of Gale-Nikaidô-Fisher-Rothenberg, and which when satisfied guarantee that the moment conditions globally identify the parameters of interest.

Fourteen leading international journals that publish econometrics articles are used to provide data on institutional activity in econometrics over the period 1980–1988. From this data base, institutional rankings are constructed separately for theoretical econometrics and all econometrics publications, according to standardized page counts of articles published in these journals. Some indication is given as to how institutional rankings have changed over this period.

This article provides a semiparametric method for the estimation of truncated regression models where the disturbances are independent of the regressors before truncation. This independence property provides useful information on model identification and estimation. Our estimate is shown to be -consistent and asymptotically normal. A consistent estimate of the asymptotic covariance matrix of the estimator is provided. Monte Carlo experiments are performed to investigate some finite sample properties of the estimator.

This paper studies a nonlinear cointegrating regression model with nonlinear nonstationary heteroskedastic error processes. We establish uniform consistency for the conventional kernel estimate of the unknown regression function and develop atwo-stage approach for the estimation of the heterogeneity generating function.

This paper considers nonstationary fractional autoregressive integrated moving-average (p,d,q) models with the fractionally differencing parameter d ∈ (− 1/2,1/2) and the autoregression function with roots on or outside the unit circle. Asymptotic inference is based on the conditional sum of squares (CSS) estimation. Under some suitable conditions, it is shown that CSS estimators exist and are consistent. The asymptotic distributions of CSS estimators are expressed as functions of stochastic integrals of usual Brownian motions. Unlike results available in the literature, the limiting distributions of various unit roots are independent of the parameter d over the entire range d ∈ (− 1/2,1/2). This allows the unit roots and d to be estimated and tested separately without loss of efficiency. Our results are quite different from the current asymptotic theories on nonstationary long memory time series. The finite sample properties are examined for two special cases through simulations.

This paper deals with issues of structure and parametrization of VECH models proposed in Bollerslev, Engle, and Wooldridge (1988) and Baba, Engle, Kraft, and Kroner (BEKK) models. Both general models and also restricted versions such as the widely used diagonal VECH (DVECH) and factor generalized autoregressive conditional heteroskedastic (F-GARCH) models are discussed. A simple algorithm is presented that checks whether a given VECH model may be cast as a BEKK model. It is shown that in the bivariate case BEKK models are as general as VECH models. In higher dimensional cases however, VECH models allow for more flexibility. In addition, a parametrization for a generic, i.e., open and dense, class of BEKK models is given, and the frequently cited parametrization by Engle and Kroner (1995, Econometric Theory 11, 122–150) is analyzed. Two shortcomings of the latter are pointed out. Finally, parametrizations for BEKK(p,q,K) models with K ≤ n, including DVECH, F-GARCH, and a generalization of the latter, are discussed.This research was supported by the project P17065 “Identification of multivariate dynamic systems with a focus on dimension reduction” of the Austrian Science Foundation (FWF).