11,578 research outputs found
Generalized Laplace inference in multiple change-points models
No full textUnder the classical long-span asymptotic framework we develop a class of Generalized Laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998). The GL estimator is defined by an integration rather than optimization-based method and relies on the least-squares criterion function. It is interpreted as a classical (non-Bayesian) estimator and the inference methods proposed retain a frequentist interpretation. This approach provides a better approximation about the uncertainty in the data of the change-points relative to existing methods. On the theoretical side, depending on some input (smoothing) parameter, the class of GL estimators exhibits a dual limiting distribution; namely, the classical shrinkage asymptotic distribution, or a Bayes-type asymptotic distribution. We propose an inference method based on Highest Density Regions using the latter distribution. We show that it has attractive theoretical properties not shared by the other popular alternatives, i.e., it is bet-proof. Simulations confirm that these theoretical properties translate to better finite-sample performance.First author draf
Continuous record Laplace-based inference about the break date in structural change models
No full textBuilding upon the continuous record asymptotic framework recently introduced by Casini and Perron (2018a) for inference in structural change models, we propose a Laplace-based (Quasi-Bayes) procedure for the construction of the estimate and confidence set for the date of a structural change. It is defined by an integration rather than an optimization-based method.A transformation of the least-squares criterion function is evaluated in order to derive a proper distribution, referred to as the Quasi-posterior. For a given choice of a loss function, the Laplace-type estimator is the minimizer of the expected risk with the expectation taken under the Quasi-posterior. Besides providing an alternative estimate that is more precise—lower mean absolute error (MAE) and lower root-mean squared error (RMSE)—than the usual least-squares one, the Quasi-posterior distribution can be used to construct asymptotically valid inference using the concept of Highest Density Region. The resulting Laplace-based inferential procedure is shown to have lower MAE and RMSE, and the confidence sets strike the best balance between empirical coverage rates and average lengths of the confidence sets relative to traditional long-span methods, whether the break size is small or large.First author draf
I. Psychologie générale : Par F. Bresson, R. Chocholle, S. Ehrlich, C. Florès, P. Jampolsky, P. Oléron, F. Orsini, R. Perron, E. Vurpillot
No full textBresson F., Chocholle R., Ehrlich Stéphane, Florès César, Jampolsky P., Oléron Pierre, Orsini F., Perron R., Vurpillot Eliane. I. Psychologie générale : Par F. Bresson, R. Chocholle, S. Ehrlich, C. Florès, P. Jampolsky, P. Oléron, F. Orsini, R. Perron, E. Vurpillot. In: L'année psychologique. 1957 vol. 57, n°1. pp. 283-293
A note on estimating and testing for multiple structural changes in models with endogenous regressors via 2SLS
No full textThis 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
Inference on locally ordered breaks in multiple regressions
No full textWe 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
GLS Detrending, Efficient Unit Root Tests and Structural Change
No full textWe extend the class of M-tests for a unit root analyzed by Perron and Ng (1996) and Ng and Perron (1997) to the case where a change in the trend function is allowed to occur at an unknown time. These tests M(GLS) adopt the GLS detrending approach of Dufour and King (1991) and Elliott, Rothenberg and Stock (1996) (ERS). Following Perron (1989), we consider two models : one allowing for a change in slope and the other for both a change in intercept and slope. We derive the asymptotic distribution of the tests as well as that of the feasible point optimal tests PT(GLS) suggested by ERS. The asymptotic critical values of the tests are tabulated. Also, we compute the non-centrality parameter used for the local GLS detrending that permits the tests to have 50% asymptotic power at that value. We show that the M(GLS) and PT(GLS) tests have an asymptotic power function close to the power envelope. An extensive simulation study analyzes the size and power in finite samples under various methods to select the truncation lag for the autoregressive spectral density estimator. An empirical application is also provided.Nous généralisons la classe de M-tests pour racine unitaire analysés par Perron et Ng (1996) et Ng et Perron (1997) au cas où la fonction de tendance peut avoir une rupture à une date inconnue. Ces tests M(GLS) utilisent la méthode des moindres carrés généralisés (MCG) pour éliminer les composantes déterministes, tel que proposé par Dufour et King (1991) et Elliot, Rothenberg et Stock (1996) (ERS). Suivant Perron (1989), nous considérons deux modèles : le premier permet une rupture dans la pente et le deuxième un changement d'ordonnée à l'origine (en plus de la rupture de la pente). Nous dérivons la distribution asymptotique des tests MGLS et celle d'une version réalisable du test optimal en un point PT(GLS) suggéré par ERS. Nous calculons aussi les valeurs critiques de ces tests. De plus, nous calculons le paramètre de non-centralité (utilisé dans l'estimation MCG pour éliminer les composantes déterministes) qui permet d'atteindre une puissance asymptotique de 50 %. Nous montrons que les tests M(GLS) et PT(GLS) ont des fonctions de puissance asymptotique proches de l'enveloppe de puissance. En utilisant des simulations, nous évaluons le niveau et la puissance des tests en échantillons finis et nous étudions plusieurs méthodes pour sélectionner le retard nécessaire pour calculer l'estimateur autorégressif de la densité spectrale. Une application à des séries de salaires réels et aux prix des actions ordinaires aux Etats-Unis est aussi considérée à la fin
GLS Detrending, Efficient Unit Root Tests and Structural Change
No full textWe extend the class of M-tests for a unit root analyzed by Perron and Ng (1996) and Ng and Perron (1997) to the case where a change in the trend function is allowed to occur at an unknown time. These tests M(GLS) adopt the GLS detrending approach of Dufour and King (1991) and Elliott, Rothenberg and Stock (1996) (ERS). Following Perron (1989), we consider two models : one allowing for a change in slope and the other for both a change in intercept and slope. We derive the asymptotic distribution of the tests as well as that of the feasible point optimal tests PT(GLS) suggested by ERS. The asymptotic critical values of the tests are tabulated. Also, we compute the non-centrality parameter used for the local GLS detrending that permits the tests to have 50% asymptotic power at that value. We show that the M(GLS) and PT(GLS) tests have an asymptotic power function close to the power envelope. An extensive simulation study analyzes the size and power in finite samples under various methods to select the truncation lag for the autoregressive spectral density estimator. An empirical application is also provided.Nous généralisons la classe de M-tests pour racine unitaire analysés par Perron et Ng (1996) et Ng et Perron (1997) au cas où la fonction de tendance peut avoir une rupture à une date inconnue. Ces tests M(GLS) utilisent la méthode des moindres carrés généralisés (MCG) pour éliminer les composantes déterministes, tel que proposé par Dufour et King (1991) et Elliot, Rothenberg et Stock (1996) (ERS). Suivant Perron (1989), nous considérons deux modèles : le premier permet une rupture dans la pente et le deuxième un changement d'ordonnée à l'origine (en plus de la rupture de la pente). Nous dérivons la distribution asymptotique des tests MGLS et celle d'une version réalisable du test optimal en un point PT(GLS) suggéré par ERS. Nous calculons aussi les valeurs critiques de ces tests. De plus, nous calculons le paramètre de non-centralité (utilisé dans l'estimation MCG pour éliminer les composantes déterministes) qui permet d'atteindre une puissance asymptotique de 50 %. Nous montrons que les tests M(GLS) et PT(GLS) ont des fonctions de puissance asymptotique proches de l'enveloppe de puissance. En utilisant des simulations, nous évaluons le niveau et la puissance des tests en échantillons finis et nous étudions plusieurs méthodes pour sélectionner le retard nécessaire pour calculer l'estimateur autorégressif de la densité spectrale. Une application à des séries de salaires réels et aux prix des actions ordinaires aux Etats-Unis est aussi considérée à la fin
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