We show that the empirical distribution of the roots of the vector autoregression (VAR) of order p fitted to T observations of a general stationary or nonstationary process converges to the uniform distribution over the unit circle on the complex plane, when both T and p tend to infinity so that (ln T)/p → 0 and p3/T → 0. In particular, even if the process is a white noise, nearly all roots of the estimated VAR will converge by absolute value to unity. For fixed p, we derive an asymptotic approximation to the expected empirical distribution of the estimated roots as T → ∞. The approximation is concentrated in a circular region in the complex plane for various data generating processes and sample sizes.

An asymptotic theory is developed for a weakly identified cointegrating regression model in which the regressor is a nonlinear transformation of an integrated process. Weak identification arises from the presence of a loading coefficient for the nonlinear function that may be close to zero. In that case, standard nonlinear cointegrating limit theory does not provide good approximations to the finite-sample distributions of nonlinear least squares estimators, resulting in potentially misleading inference. A new local limit theory is developed that approximates the finite-sample distributions of the estimators uniformly well irrespective of the strength of the identification. An important technical component of this theory involves new results showing the uniform weak convergence of sample covariances involving nonlinear functions to mixed normal and stochastic integral limits. Based on these asymptotics, we construct confidence intervals for the loading coefficient and the nonlinear transformation parameter and show that these confidence intervals have correct asymptotic size. As in other cases of nonlinear estimation with integrated processes and unlike stationary process asymptotics, the properties of the nonlinear transformations affect the asymptotics and, in particular, give rise to parameter dependent rates of convergence and differences between the limit results for integrable and asymptotically homogeneous functions.

In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment. For the sake of applications we derive the self-normalized version of this theorem. The study is motivated by models arising in economic applications where often the linear processes have long memory, and the innovations have heavy tails.

We propose a new test against a change in correlation at an unknown point in time based on cumulated sums of empirical correlations. The test does not require that inputs are independent and identically distributed under the null. We derive its limiting null distribution using a new functional delta method argument, provide a formula for its local power for particular types of structural changes, give some Monte Carlo evidence on its finite-sample behavior, and apply it to recent stock returns.

This paper introduces a new estimation method for arbitrary temporal heterogeneity in panel data models. The paper provides a semiparametric method for estimating general patterns of cross-sectional specific time trends. The methods proposed in the paper are related to principal component analysis and estimate the time-varying trend effects using a small number of common functions calculated from the data. An important application for the new estimator is in the estimation of time-varying technical efficiency considered in the stochastic frontier literature. Finite sample performance of the estimators is examined via Monte Carlo simulations. We apply our methods to the analysis of productivity trends in the U.S. banking industry.

In this article we consider a new separable nonparametric volatility model that includes second-order interaction terms in both mean and conditional variance functions. This is a very flexible nonparametric ARCH model that can potentially explain the behavior of the wide variety of financial assets. The model is estimated using the generalized version of the local instrumental variable estimation method first introduced in Kim and Linton (2004, Econometric Theory 20, 1094–1139). This method is computationally more effective than most other nonparametric estimation methods that can potentially be used to estimate components of such a model. Asymptotic behavior of the resulting estimators is investigated and their asymptotic normality is established. Explicit expressions for asymptotic means and variances of these estimators are also obtained.

We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of xt = Δ−dut, where is the fractional integration parameter and ut is weakly dependent. The classical condition is existence of q ≥ 2 and moments of the innovation sequence. When d is close to this moment condition is very strong. Our main result is to show that when and under some relatively weak conditions on ut, the existence of moments is in fact necessary for the FCLT for fractionally integrated processes and that moments are necessary for more general fractional processes. Davidson and de Jong (2000, Econometric Theory 16, 643–666) presented a fractional FCLT where only q > 2 finite moments are assumed. As a corollary to our main theorem we show that their moment condition is not sufficient and hence that their result is incorrect.

The Box–Cox regression model has been widely used in applied economics. However, there has been very limited discussion when data are censored. The focus has been on parametric estimation in the cross-sectional case, and there has been no discussion at all for the panel data model with fixed effects. This paper fills these important gaps by proposing distribution-free estimators for the Box–Cox model with censoring in both the cross-sectional and panel data settings. The proposed methods are easy to implement by combining a convex minimization problem with a one-dimensional search. The procedures are applicable to other transformation models.

We consider censored structural latent variables models where some exogenous variables are subject to additive measurement errors. We demonstrate that overidentification conditions can be exploited to provide natural instruments for the variables measured with errors, and we propose a two-stage estimation procedure. The first stage involves substituting available instruments in lieu of the variables that are measured with errors and estimating the resulting reduced form parameters using consistent censored regression methods. The second stage obtains structural form parameters using the conventional linear simultaneous equations model estimators.

An empirical likelihood–based confidence interval is proposed for interval estimations of the autoregressive coefficient of a first-order autoregressive model via weighted score equations. Although the proposed weighted estimate is less efficient than the usual least squares estimate, its asymptotic limit is always normal without assuming stationarity of the process. Unlike the bootstrap method or the least squares procedure, the proposed empirical likelihood–based confidence interval is applicable regardless of whether the underlying autoregressive process is stationary, unit root, near-integrated, or even explosive, thereby providing a unified approach for interval estimation of an AR(1) model to encompass all situations. Finite-sample simulation studies confirm the effectiveness of the proposed method.