Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence

Abstract

This article investigates the possibility, raised by Perron and by Rappoport and Reichlin, that aggregate economic time series can be characterized as being stationary around broken trend lines. Unlike those authors, we treat the break date as unknown a priori. Asymptotic distributions are developed for recursive, rolling, and sequential tests for unit roots and/or changing coefficients in time series regressions. The recursive and rolling tests are based on changing subsamples of the data. The sequential statistics are computed using the full data set and a sequence of regressors indexed by a “break” date. When applied to data on real postwar output from seven Organization for Economic Cooperation and Development countries, these techniques fail to reject the unit-root hypothesis for five countries (including the United States) but suggest stationarity around a shifted trend for Japan.