Sequential (one-by-one) rather than simultaneous estimation of multiple breaks is investigated in this paper. The advantage of this method lies in its computational savings and its robustness to misspecification in the number of breaks. The number of least-squares regressions required to compute all of the break points is of order T, the sample size. Each estimated break point is shown to be consistent for one of the true ones despite underspecification of the number of breaks. More interestingly and somewhat surprisingly, the estimated break points are shown to be T-consistent, the same rate as the simultaneous estimation. Limiting distributions are also derived. Unlike simultaneous estimation, the limiting distributions are generally not symmetric and are influenced by regression parameters of all regimes. A simple method is introduced to obtain break point estimators that have the same limiting distributions as those obtained via simultaneous estimation. Finally, a procedure is proposed to consistently estimate the number of breaks.

This paper presents central limit theorems for triangular arrays of mixingale and near-epoch-dependent random variables. The central limit theorem for near-epoch-dependent random variables improves results from the literature in various respects. The approach is to define a suitable Bernstein blocking scheme and apply a martingale difference central limit theorem, which in combination with weak dependence conditions renders the result. The most important application of this central limit theorem is the improvement of the conditions that have to be imposed for asymptotic normality of minimization estimators.

This paper compares the deterministic and stochastic predictors of nonlinear models when the disturbances are small. Large-sample properties of these predictors have been analyzed extensively in the econometric literature. While the deterministic predictors are asymptotically biased, there are some Monte Carlo experiments that suggest the magnitude of this bias is rather insignificant. Here, we offer a possible explanation of the smallness of the deterministic bias. It is shown that when the error terms have small standard deviation, the deterministic predictor turns out to be asymptotically unbiased. The results are based on deriving asymptotic expansions for alternative predictors. The asymptotic expansions carried out here are similar to the large-sample asymptotic expansions; however, the expansions here are in terms of the standard deviation of the disturbance terms. The results are then used to obtain the asymptotic bias and asymptotic mean squared prediction errors of the deterministic and stochastic predictors of a model containing the Box-Cox transformation.

This paper examines the properties of various approximation methods for solving stochastic dynamic programs in structural estimation problems. The problem addressed is evaluating the expected value of the maximum of available choices. The paper shows that approximating this by the maximum of expected values frequently has poor properties. It also shows that choosing a convenient distributional assumptions for the errors and then solving exactly conditional on the distributional assumption leads to small approximation errors even if the distribution is misspecified.

In this present paper, considering a linear regression model with nonspherical disturbances, improved confidence sets for the regression coefficients vector are developed using the Stein rule estimators. We derive the large-sample approximations for the coverage probabilities and the expected volumes of the confidence sets based on the feasible generalized least-squares estimator and the Stein rule estimator and discuss their ranking.

The Cox-Ingersoll-Ross model is a diffusion process suitable for modeling the term structure of interest rates. In this paper, we consider estimation of the parameters of this process from observations at equidistant time points. We study two estimators based on conditional least squares as well as a one-step improvement of these, two weighted conditional least-squares estimators, and the maximum likelihood estimator. Asymptotic properties of the various estimators are discussed, and we also compare their performance in a simulation study.