Improved tests for forecast comparisons in the presence of instabilities

Of interest is comparing the out-of-sample forecasting performance of two competing models in the presence of possible instabilities. To that effect, we suggest using simple structural change tests, sup-Wald and UDmax for changes in the mean of the loss differences. It is shown that Giacomini and Rossi (2010) tests have undesirable power properties, power that can be low and non-increasing as the alternative becomes further from the null hypothesis. On the contrary, our statistics are shown to have higher monotonic power, especially the UDmax version. We use their empirical examples to show the practical relevance of the issues raised

Unit roots and structural breaks

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Ultraheavy cosmic ray tracks in meteorites: A reappraisal, based on calibrations with relativistic ions

Experiments were carried out on tracks of high energy U ions in olivine, a common meteoritic mineral. The results offer an explanation for the lack of success of previous attempts to derive the Ultraheavy Cosmic Ray composition from the study of tracks in meteorites. They also suggest how such experiments should be performed. The methods tested are described and illustrated

Single-equation tests for cointegration with GLS detrended data

We provide GLS-based versions of two widely used approaches for testing whether or not non-stationary economic time series are cointegrated: single-equation static re- gression or residual-based tests and single-equation conditional error correction model (ECM) based tests. Our approach is to consider nearly optimal tests for unit roots and apply them in the cointegration context. Our GLS versions of the tests do in- deed provide substantial improvements over their OLS counterparts. We derive the local asymptotic power functions of all tests considered for a DGP with weakly ex- ogenous regressors. This allows obtaining the relevant non-centrality parameter to quasi-di§erence the data. We investigate the e§ect of non-weakly exogenous regressors via simulations. With weakly exogenous regressors strongly correlated with the depen- dent variable, the ECM tests are clearly superior. When the regressors are potentially non-weakly exogenous, the residuals-based tests are clearly preferred

Inference on locally ordered breaks in multiple regressions

We consider issues related to inference about locally ordered breaks in a system of equations, as originally proposed by Qu and Perron (2007 Qu, Z., Perron, P. (2007). Estimating and testing structural changes in multivariate regressions. Econometrica 75:459–502.[Crossref], [Web of Science ®], [Google Scholar]). These apply when break dates in different equations within the system are not separated by a positive fraction of the sample size. This allows constructing joint confidence intervals of all such locally ordered break dates. We extend the results of Qu and Perron (2007 Qu, Z., Perron, P. (2007). Estimating and testing structural changes in multivariate regressions. Econometrica 75:459–502.[Crossref], [Web of Science ®], [Google Scholar]) in several directions. First, we allow the covariates to be any mix of trends and stationary or integrated regressors. Second, we allow for breaks in the variance-covariance matrix of the errors. Third, we allow for multiple locally ordered breaks, each occurring in a different equation within a subset of equations in the system. Via some simulation experiments, we show first that the limit distributions derived provide good approximations to the finite sample distributions. Second, we show that forming confidence intervals in such a joint fashion allows more precision (tighter intervals) compared to the standard approach of forming confidence intervals using the method of Bai and Perron (1998 Bai, J., Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica 66:47–78.[Crossref], [Web of Science ®], [Google Scholar]) applied to a single equation. Simulations also indicate that using the locally ordered break confidence intervals yields better coverage rates than using the framework for globally distinct breaks when the break dates are separated by roughly 10% of the total sample size

A note on estimating and testing for multiple structural changes in models with endogenous regressors via 2SLS

This note provides a simple proof for the problem of estimating and testing for multiple breaks in a single equation framework with regressors that are endogenous. We show based on standard assumptions about the regressors, instruments, and errors that the second-stage regression of the instrumental variable procedure involves regressors and errors that satisfy all the assumptions in Perron and Qu (2006, Journal of Econometrics 134, 373–399) so that the results about consistency, rate of convergence and limit distributions of the estimates of the break dates, in addition to the limit distributions of the tests, are obtained as simple consequences. The results are obtained within a unified framework for various cases about the nature of the reduced form: stable, no structural changes but time variations in the parameters, structural changes at dates that are common to those of the structural form, and structural changes occurring at arbitrary dates.This is a revised version of parts of a paper previously circulated under the title "Estimating and Testing Multiple Structural Changes in Models with Endogenous Regressors." Perron acknowledges financial support for this work from the National Science Foundation under grant SES-0649350. We are grateful to Zhongjun Qu, two referees, the co-editor Robert Taylor and the editor Peter C. B. Phillips for useful comments. Address correspondence to Pierre Perron, Department of Economics, Boston University, 270 Bay State Rd., Boston, MA, 02215, USA; e-mail: ([email protected]). (SES-0649350 - National Science Foundation

Residuals-based tests for cointegration with generalized least-squares detrended data

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

Testing for common breaks in a multiple equations system

The issue addressed in this paper is that of testing for common breaks across or within equations. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null hypothesis is that some subsets of the parameters (either regression coe cients or elements of the covariance matrix of the errors) share one or more common break dates, with the break dates in the system asymptotically distinct so that each regime is separated by some positive fraction of the sample size. Under the alternative hypothesis, the break dates are not the same and also need not be separated by a positive fraction of the sample size. The test con- sidered is the quasi-likelihood ratio test assuming normal errors, though as usual the limit distribution of the test remains valid with non-normal errors. Also of indepen- dent interest, we provide results about the consistency and rate of convergence when searching over all possible partitions subject only to the requirement that each regime contains at least as many observations as the number of parameters in the model. Sim- ulation results show that the test has good nite sample properties. We also provide an application to various measures of in ation to illustrate its usefulness