Threshold Dynamics of Short-term Interest Rates: Empirical Evidence and Implications for the Term Structure


  • We thank one anonymous referee, Joachim Grammig, Uwe Hassler, Peter Kugler, Markku Lanne, Alberto Jurij Plazzi and Christian Schlag for helpful comments. We also thank seminar participants at the Deutsche Bundesbank, Brown Bag Finance Seminar (Goethe University Frankfurt), the ‘Workshop on Nonlinear and Nonstationary Time Series’ (2005 NBER/NSF Time Series Conference) in Heidelberg, the ‘Workshop on Nonlinear Dynamical Methods and Time Series Analysis’ in Udine 2006, the Annual Meeting of the German Economic Association in Bayreuth 2006, the 13th Annual Meeting of the German Finance Association 2006 and the 7th SAFE Center Conference ‘New Directions in Term Structure Modelling’ in Verona 2007 for discussion. This paper represents the authors' personal opinions and does not necessarily reflect the views of the Deutsche Bundesbank or its staff.


This paper studies a nonlinear one-factor term structure model in discrete time. The short-term interest rate follows a self-exciting threshold autoregressive (SETAR) process that allows for shifts in the intercept and the variance. In comparison with a linear model, we find empirical evidence in favour of the threshold model for Germany and the US. Based on the estimated short-rate dynamics we derive the implied arbitrage-free term structure of interest rates. Since analytical solutions are not feasible, bond prices are computed by means of Monte Carlo integration. The resulting term structure captures stylized facts of the data. In particular, it implies a nonlinear relation between long rates and the short rate.