Interest rate dynamics are crucial in modern economic and financial research. There has recently been an increased effort in trying to develop models of interest rate behavior. Unfortunately many of these models are based upon very restrictive assumptions: they often hypothesize that the continuous-time process followed by the instantaneous short-term interest rate is linear on its drift and has constant volatility. We study the case of two European Monetary Union participant countries where we model interest rates as converging towards a central, European rate. With nonparametric techniques we show conclusive evidence of nonlinearities in the drift and heteroskedasticity. Our results confirm those of previous nonparametric literature. Due to the special current situation of the EMU block we use as a conditioning variable the spread between the Domestic and the European short-term interest rate. We study the Italian and Spanish cases.

Key words: nonparametrics, empirical, interest rate processes, continuos time.
JEL classification: E43, C14, F36.