The Distribution of Unit Root Test Statistics After Seasonal Adjustment

• Activity Number: 675
• Type: Topic Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Tomás Del Barrio Castro*+
• Companies: University of The Balearic Islands
• Keywords: Unit root tests ; seasonality ; seasonal adjustment ; X-11 ; noninvertible moving averages ; Near Integrated proceses

Abstract

This paper argues that seasonal adjustment will generally induce noninvertible moving averages and examines the consequences for the distributions of (zero frequency) unit root test statistics for I(1) processes. The seasonal adjustment procedure analyzed is the X-11 seasonal adjustment method. Previous studies of X-11 find that seasonal adjustment has no asymptotic impact on tests under the null hypothesis of (zero frequency) integration and cointegration, but this conclusion rests on an invertibility assumption that we argue is typically invalid. As the usual unit root tests do not satisfactorily deal with noninvertible moving average components, then inferences (even asymptotically) about the presence of unit roots can be unreliable for seasonally adjusted data. We illustrate these effects analytically and through Monte Carlo simulation, for both Augmented Dickey-Fuller Phillips-Perron tests and M-type Unit root tests. Monte Carlo analysis of the large sample distributions and finite sample size properties of these unit root tests are examined for a range of seasonal and nonseasonal I(1) processes.