Estimation and Inference in Unstable Nonlinear Least Squares Models

Otilia Boldea, Alastair R. Hall

Research output: Working paper


In this paper, we extend Bai and Perron's (1998, Econometrica, pp. 47- 78) method for detecting multiple breaks to nonlinear models. To that end, we consider a nonlinear model that can be estimated via nonlinear least squares (NLS) and features a limited number of parameter shifts occurring at unknown dates. In our framework, the break-dates are estimated simultaneously with the parameters via minimization of the residual sum of squares. Using new uniform convergence results for partial sums, we derive the asymptotic distributions of both break-point and parameter estimates and propose several instability tests. We provide simulations that indicate good finite sample properties of our procedure. Additionally, we use our methods to test for misspecification of smooth-transition models in the context of an asymmetric US federal funds rate reaction function and conclude that there is strong evidence of sudden change as well as smooth behavior.
Original languageEnglish
Place of PublicationManchester
Number of pages45
Publication statusPublished - 2009

Publication series

NameCentre for Growth and Business Cycle Research
PublisherCentre for Growth and Business Cycle Research, University of Manchester


  • multiple change points, nonlinear least squares, smooth transition


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