GLS Detrending, Efficient Unit Root Tests and Structural Change

9809

PERRON, Pierre

RODRIGUEZ, Gabriel

GLS Detrending, Efficient Unit Root Tests and

Structural Change

Département de sciences économiques

Université de Montréal

Faculté des arts et des sciences C.P. 6128, succursale Centre-Ville Montréal (Québec) H3C 3J7 Canada http://www.sceco.umontreal.ca [email protected] Téléphone : (514) 343-6539 Télécopieur : (514) 343-7221

Ce cahier a également été publié par le Centre interuniversitaire de recherche en économie quantitative (CIREQ) sous le numéro 1298.

This working paper was also published by the Center for Interuniversity Research in Quantitative Economics (CIREQ), under number 1298.

CAHIER 9809

GLS DETRENDING, EFFICIENT UNIT ROOT TESTS AND STRUCTURAL CHANGE

Pierre PERRON1 and Gabriel RODRIGUEZ2

1

Centre de recherche et développement en économique (C.R.D.E.) and Département de sciences économiques, Université de Montréal, and Department of Economics, Boston University

2

C.R.D.E. and Département de sciences économiques, Université de Montréal

December 1998

_________________

This paper is drawn from chapter 1 of Gabriel Rodriguez's Ph.D. Dissertation at the Université de Montréal. The authors wish to thank Alain Guay for useful comments when this paper was presented at the 38th Annual Meeting of the Société canadienne de science économique. An earlier version was also presented at the XVI Latin American Meeting of the Econometric Society in Lima-Peru, August 12-14, 1998. Perron acknowledges financial support from the Social Sciences and Humanities Research Council (SSHRC) of Canada, the Natural Sciences and Engineering Research Council

RÉSUMÉ

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 (MGLS

) 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 (PTGLS) 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 MGLS

et GLS T

P 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.

Mots clés : test de racine unitaire, MCG, changement structurel, ordre de troncation, critère d'information

ABSTRACT

We 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 (MGLS) 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 (PTGLS) 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 MGLS

and GLS T

P 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.

Key words : unit root test, GLS detrending, structural change, truncation lag, information criteria

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