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Resistant Nonparametric Analysis of the Short Term Rate

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  • Rosario Dell'Aquila
  • Elvezio Ronchetti
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    Abstract

    Aït Sahalia (1996), Stanton (1997) and Jiang (1998) apply nonparametric and semi-parametric estimators to the short term interest rate and find strong nonlinearities in the drift function. In this paper we apply resistant techniques to the estimation of the drift and diffusion function. We show how the influential observations resulting from a resistant estimation of drift and diffusion may be used as a diagnostic tool to understand whether the estimated drift and diffusion function are broadly consistent with the assumed diffusion process. In an empirical exercise using Stanton’s (1997) and Aït-Sahalia’s (1996) data we find a clustering of influential observations in the pre 1982 period, in particular in the 1972-1974 and 1979-1982 period, suggesting that a regime change may be the dominant feature in the data rather than nonlinearities in the drift. As an additional result, we show that the bias reported in Chapman and Pearson (2000) is exaggerated because of the extrapolation of interest rate values outside the range of the simulated series.

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    Bibliographic Info

    Paper provided by Institut d'Economie et Econométrie, Université de Genève in its series Research Papers by the Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva with number 2004.06.

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    Length: 26 pages
    Date of creation: Jul 2004
    Date of revision:
    Handle: RePEc:gen:geneem:2004.06

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    1. David A. Chapman & Neil D. Pearson, 1998. "Is the Short Rate Drift Actually Nonlinear?," Finance 9808005, EconWPA.
    2. Hardle, W., 1992. "Applied Nonparametric Methods," Papers 9206, Tilburg - Center for Economic Research.
    3. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
    4. Ang, Andrew & Bekaert, Geert, 2002. "Short rate nonlinearities and regime switches," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1243-1274, July.
    5. Oliver LINTON, . "Applied nonparametric methods," Statistic und Oekonometrie 9312, Humboldt Universitaet Berlin.
    6. Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc.
    7. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-62.
    8. Haerdle,W. & Tsybakov,A., 1986. "Robust nonparametric regression with simultaneous scale curve estimation," Discussion Paper Serie A 59, University of Bonn, Germany.
    9. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 525-77.
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