Asymptotically Similar Unit Root Tests in the Presence of Autocorrelated Errors

• Activity Number: 410
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Michalis Stamatogiannis*+
• Companies: University of Groningen
• Keywords: similar critical regions ; unit root test ; size distortion ; power reversal

Abstract

The distribution of unit root test statistics generally contains nuisance parameters that correspond to the error correlation structure. This could result to serious size distortion. We adopt an approach based on the characterization of the class of asymptotically similar critical regions for the unit root hypothesis and the application of two new optimality criteria for the choice of a test within this class. The correlation structure of the error term takes the form of an MA process, the order of which is determined by information criteria. Limit distribution theory for the resulting test statistics is developed. Simulation evidence suggests that our statistics have substantially reduced size and retain good power properties. The "power reversal" problem (reduction of power as we move farther away from the null) arises for many of the widely used tests, but not for our statistics.