Resistant Nonparametric Analysis of the Short Term Rate
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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