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Threshold dynmamics of short-term interest rates: empirical evidence and implications for the term structure

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  • Archontakis, Theofanis
  • Lemke, Wolfgang

Abstract

This paper studies a nonlinear one-factor term structure model in discrete time. The single factor is the short-term interest rate, which is modeled as a self-exciting threshold autoregressive (SETAR) process. Our specification allows for shifts in the intercept and the variance. The process is stationary but mimics the nearly I(1) dynamics typically encountered with interest rates. In comparison with a linear model, we find empirical evidence in favor 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 exhibits properties that are qualitatively similar to those observed in the data and which cannot be captured by the linear Gaussian one-factor model. In particular, our model captures the nonlinear relation between long rates and the short rate found in the data.

Suggested Citation

  • Archontakis, Theofanis & Lemke, Wolfgang, 2007. "Threshold dynmamics of short-term interest rates: empirical evidence and implications for the term structure," Discussion Paper Series 1: Economic Studies 2007,02, Deutsche Bundesbank.
  • Handle: RePEc:zbw:bubdp1:5405
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    References listed on IDEAS

    as
    1. Hashem Pesaran & Davide Pettenuzzo & Allan Timmermann, 2007. "Learning, Structural Instability, and Present Value Calculations," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 253-288.
    2. Lanne, Markku & Saikkonen, Pentti, 2002. "Threshold Autoregressions for Strongly Autocorrelated Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 282-289, April.
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    More about this item

    Keywords

    Non-affine term structure models; SETAR models; Asset pricing;

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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