A Simple Specification Procedure for the Transition Function in Persistent Nonlinear Time Series Models

  • Hendrik Kaufmann
  • Robinson Kruse
  • Philipp SibbertsenEmail author


A simple procedure for the specification of the transition function describing the regime switch in nonlinear autoregressive models is proposed. This procedure is based on auxiliary regressions of unit root tests and is applicable to a variety of transition functions. In contrast to other procedures, complicated and computer-intense estimation of the candidate models is not necessary. Our approach entirely relies on OLS estimation of auxiliary regressions instead. We use standard information criteria for the selection of the unknown transition function. Our Monte Carlo simulations reveal that the approach works well in practice. Empirical applications to the S&P500 price-earnings ratio and the US interest spread highlight the merits of our suggested procedure.


Nonlinearity Smooth transition Threshold model Model selection Unit root 



The authors are grateful to the Editors of the volume for their comments and suggestions and thankful to the participants of the 20th Symposium of the Society for Nonlinear Dynamics and Econometrics in Istanbul for discussions on an earlier draft. Financial support by the Deutsche Forschungsgemeinschaft ( is gratefully acknowledged. Robinson Kruse gratefully acknowledges financial support from CREATES funded by the Danish National Research Foundation.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Hendrik Kaufmann
    • 1
  • Robinson Kruse
    • 1
    • 2
  • Philipp Sibbertsen
    • 1
    Email author
  1. 1.School of Economics and Management, Institute of StatisticsLeibniz University HannoverHannoverGermany
  2. 2.Department of Economics and Business, CREATESAarhus University, Business and Social SciencesAarhus VDenmark

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