Estimation of the intensity of a point process is considered within a nonparametric framework. The intensity measure is unknown and depends on covariates, possibly many more than the observed number of jumps. Only a single trajectory of the counting process is observed. Interest lies in estimating the intensity conditional on the covariates. The impact of the covariates is modelled by an additive model where each component can be written as a linear combination of possibly unknown functions. The focus is on prediction as opposed to variable screening. Conditions are imposed on the coefficients of this linear combination in order to control the estimation error. The rates of convergence are optimal when the number of active covariates is large. As an application, the intensity of the buy and sell trades of the New Zealand Dollar futures is estimated and a test for forecast evaluation is presented. A simulation is included to provide some finite sample intuition on the model and asymptotic properties.

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.

In this paper, we give a two-line proof of a long-standing conjecture of Ben-Akiva in his 1973 PhD thesis regarding the random utility representation of the nested logit model, thus providing a renewed and straightforward textbook treatment of that model. As an application, we provide a closed-form formula for the correlation between two Fréchet random variables coupled by a Gumbel copula.

The properties of dynamic conditional correlation (DCC) models, introduced more than a decade ago, are still not entirely known. This paper fills one of the gaps by deriving weak diffusion limits of a modified version of the classical DCC model. The limiting system of stochastic differential equations is characterized by a diffusion matrix of reduced rank. The degeneracy is due to perfect collinearity between the innovations of the volatility and correlation dynamics. For the special case of constant conditional correlations, a nondegenerate diffusion limit can be obtained. Alternative sets of conditions are considered for the rate of convergence of the parameters, obtaining time-varying but deterministic variances and/or correlations. A Monte Carlo experiment confirms that the often used quasi-approximate maximum likelihood (QAML) method to estimate the diffusion parameters is inconsistent for any fixed frequency, but that it may provide reasonable approximations for sufficiently large frequencies and sample sizes.

This paper motivates, exposits, and develops the variable augmentation specification test (VAST) approach from the perspective of generalized linear exponential family, which includes several parametric families widely used in applied econometrics and statistics. The approach is equivalent to score tests and link tests and serves to both unify and simplify the computation of score tests in such models using the Engle-Davidson-MacKinnon technique of artificial regression. Specification tests for both the mean and the variance components are treated symmetrically. Several theoretical applications are discussed.

The purpose of this paper is to differentiate between several asymptotically valid methods for confidence set construction for the autoregressive coefficient in AR(1) models. We show that the nonparametric grid bootstrap procedure suggested by Hansen (1999, Review of Economics and Statistics 81, 594–607) achieves a second order refinement in the local-to-unity asymptotic approach when compared with a modified version of Stock’s (1991, Journal of Monetary Economics 28, 435–459) and Andrews’ (1993, Econometrica 61, 139–165) grid testing procedures. We establish a second order expansion of the t-statistic in an AR(1) model in the local-to-unity asymptotic approach, which differs drastically from the usual Edgeworth-type expansions by approximating the statistic around a nonstandard and nonpivotal limit.

We consider a model Yt = σtηt in which (σt) is not independent of the noise process (ηt) but σt is independent of ηt for each t. We assume that (σt) is stationary, and we propose an adaptive estimator of the density of ln(σt2) based on the observations Yt. Under a new dependence structure, the τ-dependency defined by Dedecker and Prieur (2005, Probability Theory and Related Fields 132, 203–236), we prove that the rates of this nonparametric estimator coincide with the rates obtained in the independent and identically distributed (i.i.d.) case when (σt) and (ηt) are independent. The results apply to various linear and nonlinear general autoregressive conditionally heteroskedastic (ARCH) processes. They are illustrated by simulations applying the deconvolution algorithm of Comte, Rozenholc, and Taupin (2006, Canadian Journal of Statistics 34, 431–452) to a new noise density.

This paper considers tests in an instrumental variable (IVs) regression model with IVs that may be weak. Tests that have near-optimal asymptotic power properties with Gaussian errors for weak and strong IVs have been determined in Andrews, Moreira, and Stock (2006, Econometrica 74, 715–752). In this paper, we seek tests that have near-optimal asymptotic power with Gaussian errors and improved power with non-Gaussian errors relative to existing tests. Tests with such properties are obtained by introducing rank tests that are analogous to the conditional likelihood ratio test of Moreira (2003, Econometrica 71, 1027–1048). We also introduce a rank test that is analogous to the Lagrange multiplier test of Kleibergen (2002, Econometrica 70, 1781–1803) and Moreira (2001, manuscript, University of California, Berkeley).Andrews gratefully acknowledges the research support of the National Science Foundation via grant SES-0417911.

Statistical models of unobserved heterogeneity are typically formalized as mixtures of simple parametric models and interest naturally focuses on testing for homogeneity versus general mixture alternatives. Many tests of this type can be interpreted as C(α) tests, as in Neyman (1959), and shown to be locally asymptotically optimal. These C(α) tests will be contrasted with a new approach to likelihood ratio testing for general mixture models. The latter tests are based on estimation of general nonparametric mixing distribution with the Kiefer and Wolfowitz (1956) maximum likelihood estimator. Recent developments in convex optimization have dramatically improved upon earlier EM methods for computation of these estimators, and recent results on the large sample behavior of likelihood ratios involving such estimators yield a tractable form of asymptotic inference. Improvement in computation efficiency also facilitates the use of a bootstrap method to determine critical values that are shown to work better than the asymptotic critical values in finite samples. Consistency of the bootstrap procedure is also formally established. We compare performance of the two approaches identifying circumstances in which each is preferred.

In most cases where estimation with averaged data is performed, interest lies on the parameters of a model at the individual level, but grouped data are used because disaggregate data are not observed. In this note we study the conditions under which it is possible to consistently estimate the parameters of the individual data model using averaged data, giving particular attention to the case of endogenous selection into groups.We are grateful to an anonymous referee for helpful comments and suggestions. We also thank Pedro Duarte Neves, Les Godfrey, Paulo Parente, Maximiano Pinheiro, and Pedro Portugal for helpful discussions. The usual disclaimer applies. Machado is consultant for the Research Department of Banco de Portugal. Santos Silva is grateful for the hospitality, working conditions, and financial support provided by Banco de Portugal, which made this work possible. The authors also gratefully acknowledge partial financial support from Fundação para a Ciência e Tecnologia, program POCTI, partially funded by FEDER.

It is well known that in standard linear regression models with independent and identically distributed data and homoskedasticity, adding “irrelevant regressors” hurts (asymptotic) efficiency unless such irrelevant regressors are orthogonal to the remaining regressors. But we have found that under (conditional) heteroskedasticity “irrelevant regressors” can always be found such that one can achieve the asymptotic variance of the generalized least squares estimator by adding the “irrelevant regressors” to the model.

Standardized slowly varying regressors are shown to be Lp-approximable. This fact allows us to provide alternative proofs of asymptotic expansions of nonstochastic quantities and central limit results due to P.C.B. Phillips, under a less stringent assumption on linear processes. The recourse to stochastic calculus related to Brownian motion can be completely dispensed with.

This paper proposes a test of the rank of the submatrix of β, where β is a cointegrating matrix. In addition, the submatrix of β⊥, an orthogonal complement to β, is investigated. We construct the test statistic by using the eigenvalues of the quadratic form of the submatrix. We show that the test statistic has a limiting chi-square distribution when data are nontrending, whereas for trending data we have to consider a conservative test or other testing procedure that requires the pretest of the structure of the matrix. Finite sample simulations show that, although the simulation settings are limited, the proposed test works well for nontrending data, whereas we have to carefully use the test for trending data because it may become too conservative in some cases.I owe special thanks to two anonymous referees, the co-editor, Pierre Perron, and Taku Yamamoto. All errors are my responsibility. This research was supported by the Ministry of Education, Culture, Sports, Science and Technology under grants-in-aid 13730023 and 14203003.

In this paper, we introduce a family of contrasts for parametric inference in ARCH models the volatility of which exhibits some degeneracy. We focus specifically on ARCH processes with a linear volatility (called LARCH processes), for which the Gaussian quasi-likelihood estimator may be inconsistent. Our approach generalizes that of Beran and Schützner (2009) and gives an interesting alternative to the WLSE used by Francq and Zakoïan (2010) for an autoregressive process with LARCH errors. The family of contrasts is indexed by a single parameter that controls the smoothness of an approximated quasi-likelihood function. Under mild conditions, the resulting estimators are shown to be strongly consistent and asymptotically normal. The optimal asymptotic variance is also given. For LARCH processes, an atypical result is obtained: under assumptions, we show that the limiting distribution of the estimators can be arbitrarily close to a Gaussian distribution supported on a line. Extensions to multivariate processes are also discussed.

This paper investigates the behavior of the maximum likelihood estimator of a Gaussian autoregressive moving average model with a unit root in the moving average polynomial. The results are primarily of interest in testing hypotheses that involve moving average unit roots as, for example, when testing for stationarity of a series.

This paper considers specification testing for regression models with errors-in-variables and proposes a test statistic comparing the distance between the parametric and nonparametric fits based on deconvolution techniques. In contrast to the methods proposed by Hall and Ma (2007, Annals of Statistics, 35, 2620–2638) and Song (2008, Journal of Multivariate Analysis, 99, 2406–2443), our test allows general nonlinear regression models and possesses complementary local power properties. We establish the asymptotic properties of our test statistic for the ordinary and supersmooth measurement error densities. Simulation results endorse our theoretical findings: our test has advantages in detecting high-frequency alternatives and dominates the existing tests under certain specifications.

We extend the framework of the fully modified, ordinary least squares (OLS) estimator introduced by Phillips and Hansen (1990) to the case of seasonally cointegrated processes at a given frequency. First we extend a weak convergence result of sample covariance matrices (Phillips, 1988) to the case of seasonal unit roots. Using a complex number framework, we then show that we can take into account the constraints that exist in a situation of seasonal cointegration as illustrated in Gregoir (1999a) and derive estimates of the cointegration vectors that allow for asymptotic normal inference. This allows us to propose a test whose null hypothesis is the existence of seasonal cointegration. A Monte Carlo exercise investigates the finite sample properties of this test procedure. The paper closes with the analysis of situations in which there exist more than one frequency at which seasonal cointegration can be observed.