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.

This paper derives exact discrete time representationsfor data generated by a continuous timeautoregressive moving average (ARMA) system withmixed stock and flow data. The representations forsystems comprised entirely of stocks or of flows arealso given. In each case the discrete timerepresentations are shown to be of ARMA form, theorders depending on those of the continuous timesystem. Three examples and applications are alsoprovided, two of which concern the stationaryARMA(2, 1) model with stock variables (withapplications to sunspot data and a short-terminterest rate) and one concerning the nonstationaryARMA(2, 1) model with a flow variable (with anapplication to U.S. nondurable consumers’expenditure). In all three examples the presence ofan MA(1) component in the continuous time system hasa dramatic impact on eradicating unaccounted-forserial correlation that is present in the discretetime version of the ARMA(2, 0) specification, eventhough the form of the discrete time model isARMA(2, 1) for both models.

For many time series in empirical macro and finance, it is assumed that thelogarithm of the series is a unit root process. Since we may want to assumea stable growth rate for the macroeconomics time series, it seems natural topotentially model such a series as a unit root process with drift. Thisassumption implies that the level of such a time series is the exponentialof a unit root process with drift and therefore, it is of substantialinterest to investigate analytically the behavior of the exponential of aunit root process with drift. This paper shows that the sum of theexponential of a random walk with drift converges in distribution, afterrescaling by the exponential of the maximum value of the random walkprocess. A similar result was established in earlier work for unit rootprocesses without drift. The results derived here suggest the conjecturethat also in the case when the Dickey-Fuller test or the KPSS statistic isapplied to the exponential of a unit root process with drift, these testswill asymptotically indicate stationarity.

Consistency, asymptotic normality, and efficiency of the maximum likelihood estimator for stationary Gaussian time series were shown to hold in the short memory case by Hannan (1973, Journal of Applied Probability 10, 130–145) and in the long memory case by Dahlhaus (1989, Annals of Statistics 34, 1045–1047). In this paper we extend these results to the entire stationarity region, including the case of antipersistence and noninvertibility.

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.

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.

We propose a method, alternative to that of Estrella(2003,Econometric Theory 19,1128–1143), of obtaining exact asymptoticp-values and critical values forthe popular Andrews (1993,Econometrica 61, 821–856) testfor structural stability. The method is based oninverting an integral equation that determines theintensity of crossing a boundary by the asymptoticprocess underlying the test statistic. Furtherintegration of the crossing intensity yields ap-value. The proposed method canpotentially be applied to other stability tests thatemploy the supremum functional.

This paper considers the problem of variance estimation for the sample mean in the context of long memory and negative memory time series dynamics, adopting the fixed-bandwidth approach now popular in the econometrics literature. The distribution theory generalizes the short memory results of Kiefer and Vogelsang (2005, Econometric Theory 21, 1130–1164). In particular, our results highlight the dependence on the kernel (we include flat-top kernels), whether or not the kernel is nonzero at the boundary, and, most important, whether or not the process is short memory. Simulation studies support the importance of accounting for memory in the construction of confidence intervals for the mean.

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.

This note demonstrates that the conditions of Kotlarski’s (1967, Pacific Journal of Mathematics 20(1), 69–76) lemma can be substantially relaxed. Inparticular, the condition that the characteristic functions of M, U1, and U2 are nonvanishing can be replaced with muchweaker conditions: The characteristic function of U1 can be allowed to have real zeros, as longas the derivative of its characteristic function at those points is not alsozero; that of U2 can have an isolated number ofzeros; and that of M need satisfy no restrictions on itszeros. We also show that Kotlarski’s lemma holds when the tails of U1 are no thicker than exponential,regardless of the zeros of the characteristic functions of U1, U2, or M.

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.