http://repub.eur.nl/res/aut/10186/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/11369/ 2003-12-01T00:00:00Z http://repub.eur.nl/res/pub/2064/ 1997-01-01T00:00:00Z In this paper we propose a model selection strategy for a univariate periodic autoregressive time series which involves tests for one or more unit roots and for parameter restrictions corresponding to seasonal unit roots and multiple unit roots at the zero frequency. Examples of models that are considered are variants of the seasonal unit roots model and the periodic integration model. We show that the asymptotic distributions of various test statistics are the same as well-known distributions which are already tabulated. We apply our strategy to three empirical series to illustrate its ease of use. We find that evidence for seasonal unit roots based on nonperiodic models disappears when periodic representations are considered. http://repub.eur.nl/res/pub/2078/ 1994-01-01T00:00:00Z The properties of the univariate Dickey-Fuller test and the Johansen test for the cointegrating rank when there exist additive outlying observations in the time series are examined. The analysis provides analytical as well as numerical evidence that additive outliers may produce spurious stationarity. Hence, the Dickey-Fuller test will reject a unit root too frequently, and the Johansen test will indicate too many cointegrating vectors. The results easily generalize to models with temporary change outliers. Through an empirical example, the analysis demonstrates how additive and temporary change outliers can be detected in practice, and it shows how dummy variables can be used to remove the influence of such extreme observations. A proper statistical procedure to detect outliers is necessary. Many statistical software packages for analyzing autoregressive integrating moving average models have built-in routines to detect outliers.