Journal of Econometrics 62 (1994) 211-228. North Holland Testing the constancy of regression parameters against continuous structural change* Chien-Fu Jeff Lin zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGF Nutional Taiwan University, Taipei 104, Taiwan, ROC Timo Terkirta Bank qf‘ zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Norway, N-0107 Oslo, Nowa) Received October 1991, final version received March 1993 A standard explicit or implicit assumption underlying many parameter constancy tests in linear models is that there is a single structural break in the sample. In this paper that assumption is replaced by a more general one stating that the parameters of the model may change continuously over time. The pattern of change is parameterized giving rise to a set of parameter constancy tests against a parameterized alternative. The power properties of the LM type tests in small samples are compared to those of other tests like the CUSUM and Fluctuation Test by simulation and found very satisfactory. An application is considered. Keywords: Lagrange multiplier test; Nonlinear regression; Smooth transition regression; Structural break JEL classijication: C22; C52 Correspondence to: Timo Terisvirta, Research Department, Bank of Norway, PB 1179 Sentrum, N-0107 Oslo, Norway. *The work for the paper was carried out while the first author was a student and the second author a visiting scholar at the University of California, San Diego. They are grateful to all the econometricians there for providing such a stimulating research atmosphere. Earlier versions of the paper were presented at the North American Summer Meeting of the Econometric Society, Philadelphia, June 1991, the (EC)* conference, Rotterdam, December 1991, the Econometric Society European Meeting, Brussels, August 1992, and in seminars at Chalmers University of Technology, Copenhagen, European University Institute (Florence), Stockholm, Tartu, and Uppsala. The authors wish to thank the participants of the meetings and seminars and Chia-Shang James Chu, Jan de Gooijer, Clive Granger, Lars-Erik Oiler, Pentti Saikkonen, Pierre Perron, Pierre Siklos, Ching-Zong Wei, Halbert White, and two anonymous referees for helpful comments. Any errors and shortcomings are the sole responsibility of the authors. The second author acknowledges financial support from the Yrja Jahnsson Foundation and the Swedish Council of Economic Advisors. 0304-4076/94/$07.00 9 1994-Elsevier Science B.V. All rights reserved