In this paper we propose a bootstrap version of theWald test for cointegration in a single-equationconditional error correction model. The multivariatesieve bootstrap is used to deal with dependence inthe series. We show that the introduced bootstraptest is asymptotically valid. We also analyze thesmall sample properties of our test by simulationand compare it with the asymptotic test and severalalternative bootstrap tests. The bootstrap testoffers significant improvements in terms of sizeproperties over the asymptotic test, while havingsimilar power properties. The sensitivity of thebootstrap test to the allowance for deterministiccomponents is also investigated. Simulation resultsshow that the tests with sufficient deterministiccomponents included are insensitive to the truevalue of the trends in the model and retain correctsize.

This paper develops tests for the null hypothesis ofcointegration in the nonlinear regression model withI(1) variables. The teststatistics we use in this paper are Kwiatkowski,Phillips, Schmidt, and Shin’s (1992; KPSS hereafter)tests for the null of stationarity, though usingother kinds of tests is also possible. The tests areshown to depend on the limiting distributions of theestimators and parameters of the nonlinear modelwhen they use full-sample residuals from thenonlinear least squares and nonlinear leads-and-lagsregressions. This feature makes it difficult to usethem in practice. As a remedy, this paper developstests using subsamples of the regression residuals.For these tests, first, the nonlinear least squaresand nonlinear leads-and-lags regressions are run andresiduals are calculated. Second, the KPSS tests areapplied using subresiduals of sizeb. As long asb/T → 0 asT → ∞, where Tis the sample size, the tests using the subresidualshave limiting distributions that are not affected bythe limiting distributions of the full-sampleestimators and the parameters of the model. Third,the Bonferroni procedure is used for a selectednumber of the subresidual-based tests. Monte Carlosimulation shows that the tests work reasonably wellin finite samples for polynomial and smoothtransition regression models when the block size ischosen by the minimum volatility rule. Inparticular, the subresidual-based tests using theleads-and-lags regression residuals appear to bepromising for empirical work. An empirical examplestudying the U.S. money demand equation illustratesthe use of the tests.

The two most popular bandwidth choice rules for kernelHAC estimation have been proposed by Andrews (1991)and Newey and West (1994). This paper suggests analternative approach that estimates an unknownquantity in the optimal bandwidth for the HACestimator (called normalizedcurvature) using a general class ofkernels, and derives the optimal bandwidth thatminimizes the asymptotic mean squared error of theestimator of normalized curvature. It is shown thatthe optimal bandwidth for the kernel-smoothednormalized curvature estimator should diverge at aslower rate than that of the HAC estimator using thesame kernel. An implementation method of the optimalbandwidth for the HAC estimator, which is analogousto the one for probability density estimation bySheather and Jones (1991), is also developed. Thefinite sample performance of the new bandwidthchoice rule is assessed through Monte Carlosimulations.

This article investigates model checks for a class ofpossibly nonlinear heteroskedastic time seriesmodels, including but not restricted to ARMA-GARCHmodels. We propose omnibus tests based onfunctionals of certain weighted standardizedresidual empirical processes. The new tests areasymptotically distribution-free, suitable when theconditioning set is infinite-dimensional, andconsistent against a class of Pitman’s localalternatives converging at the parametric raten−1/2, withn the sample size. A Monte Carlostudy shows that the simulated level of the proposedtests is close to the asymptotic level already formoderate sample sizes and that tests have asatisfactory power performance. Finally, weillustrate our methodology with an application tothe well-known S&P 500 daily stock index. Thepaper also contains an asymptotic uniform expansionfor weighted residual empirical processes wheninitial conditions are considered, a result ofindependent interest.

Assume that observations are generated fromnonstationary autoregressive (AR) processes ofinfinite order. We adopt a finite-orderapproximation model to predict future observationsand obtain an asymptotic expression for themean-squared prediction error (MSPE) of the leastsquares predictor. This expression provides thefirst exact assessment of the impacts ofnonstationarity, model complexity, and modelmisspecification on the corresponding MSPE. It notonly provides a deeper understanding of the leastsquares predictors in nonstationary time series, butalso forms the theoretical foundation for acompanion paper by the same authors, which obtainsasymptotically efficient order selection innonstationary AR processes of possibly infiniteorder.

Linearity in a causal relationship between a dependentvariable and a set of regressors is a commonassumption throughout economics. In this paper weconsider the case when the coefficients in thisrelationship are random and distributedindependently from the regressors. Our aim is toidentify and estimate the distribution of thecoefficients nonparametrically. We propose akernel-based estimator for the joint probabilitydensity of the coefficients. Although this estimatorshares certain features with standard nonparametrickernel density estimators, it also differs in someimportant characteristics that are due to the verydifferent setup we are considering. Mostimportantly, the kernel is nonstandard and derivesfrom the theory of Radon transforms. Consequently,we call our estimator the Radon transform estimator(RTE). We establish the large sample behavior ofthis estimator—in particular, rate optimality andasymptotic distribution. In addition, we extend thebasic model to cover extensions, includingendogenous regressors and additional controls.Finally, we analyze the properties of the estimatorin finite samples by a simulation study, as well asan application to consumer demand using Britishhousehold data.

This paper considers a formulation of the extendedconstant or time-varying conditional correlationGARCH model that allows for volatility feedback ofeither the positive or negative sign. In theprevious literature, negative volatility spilloverswere ruled out by the assumption that all theparameters of the model are nonnegative, which is asufficient condition for ensuring the positivedefiniteness of the conditional covariance matrix.In order to allow for negative feedback, we showthat the positive definiteness of the conditionalcovariance matrix can be guaranteed even if some ofthe parameters are negative. Thus, we extend theresults of Nelson and Cao (1992) and Tsai and Chan(2008) to a multivariate setting. For the bivariatecase of order one, we look into the consequences ofadopting these less severe restrictions and findthat the flexibility of the process is substantiallyincreased. Our results are helpful for themodel-builder, who can consider the unrestrictedformulation as a tool for testing various economictheories.

We study a nonlinear panel data model in which thefixed effects are assumed to have finite support.The fixed effects estimator is known to have theincidental parameters problem. We contribute to theliterature by making a qualitative observation thatthe incidental parameters problem in this model maynot be not as severe as in the conventional case.Because fixed effects have finite support, theprobability of correctly identifying the fixedeffect converges to one even when the crosssectional dimension grows as fast as someexponential function of the time dimension. As aconsequence, the finite sample bias of the fixedeffects estimator is expected to be small.

A vector autoregressive model allowing for unit rootsas well as an explosive characteristic root isdeveloped. The Granger-Johansen representation showsthat this results in processes with two commonfeatures: a random walk and an explosively growingprocess. Cointegrating and coexplosive vectors canbe found that eliminate these common factors. Thelikelihood ratio test for a simple hypothesis on thecoexplosive vectors is analyzed. The method isillustrated using data from the extreme Yugoslavianhyperinflation of the 1990s.

We derive a closed-form expression for the asymptoticdistribution of the LIML estimator for thecoefficients of both endogenous and exogenousvariables in a partially identified linearstructural equation. We extend previous results ofPhillips (1989) and Choi and Phillips (1992), wherethe focus was on IV estimators. We show that partialfailure of identification affects the LIML in thatits moments do not exist even asymptotically.

In this paper, we propose nonparametric estimators ofsharp bounds on the distribution of treatmenteffects of a binary treatment and establish theirasymptotic distributions. We note the possiblefailure of the standard bootstrap with the samesample size and apply thefewer-than-n bootstrap to makinginferences on these bounds. The finite sampleperformances of the confidence intervals for thebounds based on normal critical values, the standardbootstrap, and the fewer-than-nbootstrap are investigated via a simulation study.Finally we establish sharp bounds on the treatmenteffect distribution when covariates areavailable.

Least absolute deviations (LAD) estimation of lineartime series models is considered under conditionalheteroskedasticity and serial correlation. The limittheory of the LAD estimator is obtained withoutassuming the finite density condition for the errorsthat is required in standard LAD asymptotics. Theresults are particularly useful in application ofLAD estimation to financial time series data.