We provide generalized least‐squares (GLS) detrended versions of single‐equation static regression or residuals‐based tests for testing whether or not non‐stationary time series are cointegrated. Our approach is to consider nearly optimal tests for unit roots and to apply them in the cointegration context. We derive the local asymptotic power functions of all tests considered for a triangular data‐generating process, imposing a directional restriction such that the regressors are pure integrated processes. Our GLS versions of the tests do indeed provide substantial power improvements over their ordinary least‐squares counterparts. Simulations show that the gains in power are important and stable across various configurations.

In this paper, we develop a general method of testing for independence when unobservable generalized errors are involved. Our method can be applied to testing for serial independence of generalized errors, and testing for independence between the generalized errors and observable covariates. The former can serve as a unified approach to testing the adequacy of time series models, as model adequacy often implies that the generalized errors obtained after a suitable transformation are independent and identically distributed. The latter is a key identification assumption in many nonlinear economic models. Our tests are based on a classical sample dependence measure, the Hoeffding–Blum–Kiefer–Rosenblatt‐type empirical process applied to generalized residuals. We establish a uniform expansion of the process, thereby deriving an explicit expression for the parameter estimation effect, which causes our tests not to be nuisance‐parameter‐free. To circumvent this problem, we propose a multiplier‐type bootstrap to approximate the limit distribution. Our bootstrap procedure is computationally very simple as it does not require a re‐estimation of the parameters in each bootstrap replication. Simulations and empirical applications to daily exchange rate data highlight the merits of our approach.

Journal Article Index to The Econometrics Journal Volume 18 Get access The Econometrics Journal, Volume 18, Issue 3, 1 October 2015, Page 437, https://doi.org/10.1111/ectj.12057 Published: 23 December 2015

Journal Article Heteroscedasticity‐robust Cp model averaging Get access Qingfeng Liu, Qingfeng Liu Department of Economics, Otaru University of Commerce, 5-21, Midori 3-chome, Otaru, Hokkaido 047-8501, Japan Search for other works by this author on: Oxford Academic Google Scholar Ryo Okui Ryo Okui Institute of Economic Research, Kyoto University, Yoshida-Hommachi, Sakyo, Kyoto Kyoto 606-8501, Japan Search for other works by this author on: Oxford Academic Google Scholar The Econometrics Journal, Volume 16, Issue 3, 1 October 2013, Pages 463–472, https://doi.org/10.1111/ectj.12009 Published: 22 November 2013 Article history Received: 01 March 2012 Accepted: 01 April 2013 Published: 22 November 2013

This paper proposes a model-free cotrending rank selection procedure based on the eigenstructure of a multivariate version of the von Neumann ratio, in the presence of both stochastic and nonlinear deterministic trends. Our selection criteria are easily implemented, and the consistency of the rank estimator is established under very general conditions. Simulation results suggest good …nite sample properties of the new rank selection criteria. The proposed method is then illustrated through an application of the Japanese money demand function allowing for the cotrending relationship among money, income and interest rates.

Summary The inference of the threshold point in threshold models critically depends on the assumption that the density of the threshold variable at the true threshold point is continuous and bounded away from zero and infinity. However, violation of this assumption may arise in several econometric contexts such as treatment effects evaluation. This paper presents a thorough characterisation of the asymptotic distributions in the least-squares estimation of such abnormal cases. First, the asymptotic results on the threshold point are different from the conventional case. For example, any convergence rate between zero and infinity is possible; the asymptotic distribution can be discrete, continuous or a mixture of discrete and continuous; the weak limits of the localised objective functions can be non-homogeneous instead of homogeneous compound Poisson processes. Second, this paper distinguishes threshold regression from structural change models by studying a problem unique in threshold regression. Third, the asymptotic distributions of regular parameters are not affected by estimation of the threshold point irrespective of the density of the threshold variable. Numerical calculations and simulation results confirm the theoretical analysis, and the density of the threshold variable in an application is checked to illustrate the relevance of the study in this paper.

The paper develops a new heteroskedasticity and autocorrelation robust test in a time series setting. The test is based on a series long‐run variance matrix estimator that involves projecting the time series of interest onto a set of orthonormal bases and using the sample variance of the projection coefficients as the long‐run variance estimator. When the number of orthonormal bases K is fixed, a finite‐sample‐corrected Wald statistic converges to a standard F distribution. When K grows with the sample size, the usual uncorrected Wald statistic converges to a chi‐square distribution. We show that critical values from the F distribution are second‐order correct under the conventional increasing smoothing asymptotics. Simulations show that the F approximation is more accurate than the chi‐square approximation in finite samples.

Summary We suggest and compare different methods for estimating spatial autoregressive models with randomly missing data in the dependent variable. Aside from the traditional expectation-maximization (EM) algorithm, a nonlinear least squares method is suggested and a generalized method of moments estimation is developed for the model. A two-stage least squares estimation with imputation is proposed as well. We analytically compare these estimation methods and find that generalized nonlinear least squares, best generalized two-stage least squares with imputation and best method of moments estimators have identical asymptotic variances. These methods are less efficient than maximum likelihood estimation implemented with the EM algorithm. When unknown heteroscedasticity exists, however, EM estimation produces inconsistent estimates. Under this situation, these methods outperform EM. We provide finite sample evidence through Monte Carlo experiments.