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Unit root tests with level shift in the presence of GARCH.

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Disciplines
  • Economics

Abstract

PII: 0165-1765(95)00654-X economics letters EI.SEVIER Economics Letters 49 (1995) 125-130 Unit root tests with level shift in the presence of GARCH Alain Hecq Service des Etudes et de la Statistique (S.E.S.), Minist&e de la Rdgion Wallonne. Place de la Wallonie 1, 5100 Jambes, Belgium Received 9 February 1994; revised version received 12 December 1994; accepted 4 January 1995 Abstract The aim of this paper is to examine, using Monte Carlo experiments, the behaviour of unit root tests with a changing mean at an unknown date (Perron and Vogelsang, Journal of Business and Economic Statistics, 1992, 10, 301-320), in the presence of IGARCH errors. We find that the empirical sizes of the test statistics are significantly above the nominal ones and that distortions are considerably amplified by a conditional Student's t distribution instead of a normal one. Keywords: Unit root; Breaking mean; GARCH JEL classification: C22 1. Motivations Through Monte Carlo experiments, the behaviour of the most frequently used unit root tests (Dickey-Fuller, Phillips-Perron) in the presence of GARCH errors is already well documented. Haldrup (1992), Kim and Schmidt (1993), Urbain (1991) stress the fact that, if GARCH time series are better characterized by a small volatility parameter and a large moving average parameter, the size distortions can be small. Hecq and Urbain (1993b) take into account IGARCH processes that are not simultaneously degenerated and show that a Student's t conditional distribution instead of the normal one can lead to less optimistic conclusions. In the spirit of those studies, Monte Carlo experiments are used in this paper to analyse the behaviour of unit root tests with a changing mean, in the presence of IGARCH errors. Indeed, faced with a deterministic changing mean or breaking trend, Perron (1989, 1990a) and Rappoport and Reichlin (1989) show that the Dickey-Fuller unit root tests are biased, even asymptotically, towards non-rejection of t

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