We show that the empirical distribution of the roots ofthe vector autoregression (VAR) of orderp fitted to Tobservations of a general stationary ornonstationary process converges to the uniformdistribution over the unit circle on the complexplane, when both T andp tend to infinity so that (lnT)/p → 0 andp3/T→ 0. In particular, even if the process is a whitenoise, nearly all roots of the estimated VAR willconverge by absolute value to unity. For fixedp, we derive an asymptoticapproximation to the expected empirical distributionof the estimated roots as T → ∞.The approximation is concentrated in a circularregion in the complex plane for various datagenerating processes and sample sizes.

An asymptotic theory is developed for a weaklyidentified cointegrating regression model in whichthe regressor is a nonlinear transformation of anintegrated process. Weak identification arises fromthe presence of a loading coefficient for thenonlinear function that may be close to zero. Inthat case, standard nonlinear cointegrating limittheory does not provide good approximations to thefinite-sample distributions of nonlinear leastsquares estimators, resulting in potentiallymisleading inference. A new local limit theory isdeveloped that approximates the finite-sampledistributions of the estimators uniformly wellirrespective of the strength of the identification.An important technical component of this theoryinvolves new results showing the uniform weakconvergence of sample covariances involvingnonlinear functions to mixed normal and stochasticintegral limits. Based on these asymptotics, weconstruct confidence intervals for the loadingcoefficient and the nonlinear transformationparameter and show that these confidence intervalshave correct asymptotic size. As in other cases ofnonlinear estimation with integrated processes andunlike stationary process asymptotics, theproperties of the nonlinear transformations affectthe asymptotics and, in particular, give rise toparameter dependent rates of convergence anddifferences between the limit results for integrableand asymptotically homogeneous functions.

In this paper we study the convergence to fractionalBrownian motion for long memory time series havingindependent innovations with infinite second moment.For the sake of applications we derive theself-normalized version of this theorem. The studyis motivated by models arising in economicapplications where often the linear processes havelong memory, and the innovations have heavytails.

We propose a new test against a change in correlationat an unknown point in time based on cumulated sumsof empirical correlations. The test does not requirethat inputs are independent and identicallydistributed under the null. We derive its limitingnull distribution using a new functional deltamethod argument, provide a formula for its localpower for particular types of structural changes,give some Monte Carlo evidence on its finite-samplebehavior, and apply it to recent stock returns.

This paper introduces a new estimation method forarbitrary temporal heterogeneity in panel datamodels. The paper provides a semiparametric methodfor estimating general patterns of cross-sectionalspecific time trends. The methods proposed in thepaper are related to principal component analysisand estimate the time-varying trend effects using asmall number of common functions calculated from thedata. An important application for the new estimatoris in the estimation of time-varying technicalefficiency considered in the stochastic frontierliterature. Finite sample performance of theestimators is examined via Monte Carlo simulations.We apply our methods to the analysis of productivitytrends in the U.S. banking industry.

In this article we consider a new separablenonparametric volatility model that includessecond-order interaction terms in both mean andconditional variance functions. This is a veryflexible nonparametric ARCH model that canpotentially explain the behavior of the wide varietyof financial assets. The model is estimated usingthe generalized version of the local instrumentalvariable estimation method first introduced in Kimand Linton (2004, Econometric Theory20, 1094–1139). This method is computationally moreeffective than most other nonparametric estimationmethods that can potentially be used to estimatecomponents of such a model. Asymptotic behavior ofthe resulting estimators is investigated and theirasymptotic normality is established. Explicitexpressions for asymptotic means and variances ofthese estimators are also obtained.

We discuss the moment condition for the fractionalfunctional central limit theorem (FCLT) for partialsums of xt =Δ−dut,where isthe fractional integration parameter andut is weaklydependent. The classical condition is existence ofq ≥ 2 and moments of the innovation sequence. Whend is close to thismoment condition is very strong. Our main result isto show that when and undersome relatively weak conditions onut, the existence ofmoments is in fact necessary for the FCLT forfractionally integrated processes and thatmoments are necessary for more general fractionalprocesses. Davidson and de Jong (2000,Econometric Theory 16, 643–666)presented a fractional FCLT where onlyq > 2 finite moments areassumed. As a corollary to our main theorem we showthat their moment condition is not sufficient andhence that their result is incorrect.

The Box–Cox regression model has been widely used inapplied economics. However, there has been verylimited discussion when data are censored. The focushas been on parametric estimation in thecross-sectional case, and there has been nodiscussion at all for the panel data model withfixed effects. This paper fills these important gapsby proposing distribution-free estimators for theBox–Cox model with censoring in both thecross-sectional and panel data settings. Theproposed methods are easy to implement by combininga convex minimization problem with a one-dimensionalsearch. The procedures are applicable to othertransformation models.

We consider censored structural latent variables modelswhere some exogenous variables are subject toadditive measurement errors. We demonstrate thatoveridentification conditions can be exploited toprovide natural instruments for the variablesmeasured with errors, and we propose a two-stageestimation procedure. The first stage involvessubstituting available instruments in lieu of thevariables that are measured with errors andestimating the resulting reduced form parametersusing consistent censored regression methods. Thesecond stage obtains structural form parametersusing the conventional linear simultaneous equationsmodel estimators.

An empirical likelihood–based confidence interval isproposed for interval estimations of theautoregressive coefficient of a first-orderautoregressive model via weighted score equations.Although the proposed weighted estimate is lessefficient than the usual least squares estimate, itsasymptotic limit is always normal without assumingstationarity of the process. Unlike the bootstrapmethod or the least squares procedure, the proposedempirical likelihood–based confidence interval isapplicable regardless of whether the underlyingautoregressive process is stationary, unit root,near-integrated, or even explosive, therebyproviding a unified approach for interval estimationof an AR(1) model to encompass all situations.Finite-sample simulation studies confirm theeffectiveness of the proposed method.