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

53 Pages Posted: 13 Nov 2007 Last revised: 6 Aug 2022

See all articles by Anindya Banerjee

Anindya Banerjee

European University Institute - Department of Economics; University of Oxford - Department of Economics

Robin L. Lumsdaine

American University - Department of Finance and Real Estate; Erasmus University Rotterdam (EUR) - Department of Econometrics; National Bureau of Economic Research (NBER); Tinbergen Institute

James H. Stock

Harvard University - Department of Economics; National Bureau of Economic Research (NBER); Harvard University - Harvard Kennedy School (HKS)

Date Written: November 1990

Abstract

This paper investigates the possibility, raised by Perron (1989, 1990a), that aggregate economic time series can be characterized as being stationary around broken trend lines. Unlike Perron, 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 a time series of recursively estimated coefficients, computed using increasing 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 DECO countries, these techniques fail to reject the unit root hypothesis for five countries (including the U.S.), but suggest stationarity around a shifted trend for Japan.

Suggested Citation

Banerjee, Anindya and Lumsdaine, Robin L. and Stock, James H., Recursive and Sequential Tests of the Unit Root and Trend Break Hypothesis: Theory and International Evidence (November 1990). NBER Working Paper No. w3510, Available at SSRN: https://ssrn.com/abstract=471510

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