Local linear fitting is a popular nonparametric method in statistical and econometric modeling. Lu and Linton (2007, Econometric Theory23, 37–70) established the pointwise asymptotic distribution for the local linear estimator of a nonparametric regression function under the condition of near epoch dependence. In this paper, we further investigate the uniform consistency of this estimator. The uniform strong and weak consistencies with convergence rates for the local linear fitting are established under mild conditions. Furthermore, general results regarding uniform convergence rates for nonparametric kernel-based estimators are provided. The results of this paper will be of wide potential interest in time series semiparametric modeling.

Economic data are frequently generated by stochastic processes that can be modeled as realizations of random functions (functional data). This paper adapts the specification test for functional data developed by Bugni, Hall, Horowitz, and Neumann (2009, Econometrics Journal12, S1–S18) to the presence of missing observations. By using a worst case scenario approach, our method is able to extract the information available in the observed portion of the data while being agnostic about the nature of the missing observations. The presence of missing data implies that our test will not only result in the rejection or lack of rejection of the null hypothesis, but it may also be inconclusive.

Under the null hypothesis, our specification test will reject the null hypothesis with a probability that, in the limit, does not exceed the significance level of the test. Moreover, the power of the test converges to one whenever the distribution of the observations conveys that the null hypothesis is false.

Monte Carlo evidence shows that the test may produce informative results (either rejection or lack of rejection of the null hypothesis) even under the presence of significant amounts of missing data. The procedure is illustrated by testing whether the Burdett–Mortensen labor market model is the correct framework for wage paths constructed from the National Longitudinal Survery of Youth, 1979 survey.

This paper considers a moments-based nonlinear estimator that is $\root \of T $-consistent and uniformly asymptotically normal irrespective of the degree of persistence of the forcing process. These properties hold for linear autoregressive models, linear predictive regressions, and certain nonlinear dynamic models. Asymptotic normality is obtained because the moments are chosen so that the objective function is uniformly bounded in probability and so that a central limit theorem can be applied. Critical values from the normal distribution can be used irrespective of the treatment of the deterministic terms. Simulations show that the estimates are precise and the t-test has good size in the parameter region where the least squares estimates usually yield distorted inference.

We consider a rank-based technique for estimating generalized autoregressive conditionally heteroskedastic (GARCH) model parameters, some of which are scale transformations of conventional GARCH parameters. The estimators are obtained by minimizing a rank-based residual dispersion function similar to the one given in Jaeckel (1972, Annals of Mathematical Statistics43, 1449–1458). They are useful for GARCH order selection and preliminary estimation. We give a limiting distribution for the rank estimators that holds when the true parameter vector is in the interior of its parameter space and when some GARCH parameters are zero. The limiting theory is used to show that the rank estimators are robust, can have the same asymptotic efficiency as maximum likelihood estimators, and are relatively efficient compared to traditional Gaussian and Laplace quasi-maximum likelihood estimators. The behavior of the estimators for finite samples is studied via simulation, and we use rank estimation to fit a GARCH model to exchange rate log-returns.

This paper investigates the global self-weighted least absolute deviation (SLAD) estimator for finite and infinite variance ARMA(p, q) models. The strong consistency and asymptotic normality of the global SLAD estimator are obtained. A simulation study is carried out to assess the performance of the global SLAD estimators. In this paper the asymptotic theory of the global LAD estimator for finite and infinite variance ARMA(p, q) models is established in the literature for the first time. The technique developed in this paper is not standard and can be used for other time series models.

Microeconomic theory often yields models with multiple nonlinear equations, nonseparable unobservables, nonlinear cross equation restrictions, and many potentially multicolinear covariates. We show how statistical dimension reduction techniques can be applied in models with these features. In particular, we consider estimation of derivatives of average structural functions in large consumer demand systems, which depend nonlinearly on the prices of many goods. Utility maximization imposes nonlinear cross equation constraints including Slutsky symmetry, and preference heterogeneity yields demand functions that are nonseparable in unobservables. The standard method of achieving dimension reduction in demand systems is to impose strong, empirically questionable economic restrictions such as separability. In contrast, the validity of statistical methods of dimension-reduction such as principal components has not hitherto been studied in contexts like these. We derive the restrictions implied by utility maximization on dimension-reduced demand systems and characterize the implications for identification and estimation of structural marginal effects. We illustrate the results by reporting estimates of the effects of gasoline prices on the demands for many goods, without imposing any economic separability assumptions.

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.

In this paper, we propose a new diagnostic test for residual cross-section uncorrelatedness (CU) in a nonparametric panel data model. The proposed nonparametric CU test is a nonparametric counterpart of an existing parametric cross-section dependence test proposed in Pesaran (2004, Cambridge Working paper in Economics 0435). Without assuming cross-section independence, we establish asymptotic distribution for the proposed test statistic for the case where both the cross-section dimension and the time dimension go to infinity simultaneously, and then analyze the power function of the proposed test under a sequence of local alternatives that involve a nonlinear multifactor model. The simulation results and real data analysis show that the nonparametric CU test associated with an asymptotic critical value works well.