Unit Root Tests in the Presence of Innovational Outliers

Abstract

Unit root tests are considered for time series with innovational outliers. The function representing the outliers can have a very general nonlinear form and additional deterministic mean and trend terms are allowed for. Prior to the tests the deterministic parts and other nuisance parameters of the data generation process are estimated in a first step. Then the series are adjusted for these terms and unit root tests of the Dickey-Fuller type are applied to the adjusted series. The properties of previously suggested tests of this sort are analyzed and modifications are proposed which take into account estimation errors in the nuisance parameters. An important result is that estimation under the null hypothesis is preferable to estimation under local alternatives. This contrasts with results obtained by other authors for time series without outliers. A comparison with additive outlier models is also performed.

We are grateful to Ralf Brüggemann for helping with the computations and to Christian Müller for comments. Moreover, we thank the Deutsche Forschungsgemeinschaft, SFB 373, the European Commission under the Training and Mobility of Researchers Programme (contract No. ERBFMRXCT980213) and the Yrjö Jahnsson Foundation for financial support. The third author also acknowledges financial support by the Alexander von Humboldt Foundation under a Humboldt research award. Part of this research was done while the first and third authors were visiting and the second author was affiliated with the Humboldt University in Berlin.