This article attempts to identify the best features the short term interest rates stochastic process. We studied nine different linear models of short term interest rates. The choice of these models was the aim of analyzing the relevance of certain specifications of the short term interest rate stochastic process, the effect of mean reversion and the sensitivity of the volatility to the level of interest rate. We studied also the relevance of the Ait-Sahalia (1996b) nonlinear interest rate model. To further study the accurate parametric specification of the interest rate stochastic process we used a nonparametric estimation of the drift and the diffusion functions.The yield on three months treasury bills is used as a proxy for the short term interest rates. The parameters of the different linear stochastic process are estimated using the generalized method of moments. A semi parametric approach is used to estimate the non linear Ait Sahalia model (1996b). The kernel regression is used as a nonparametric approach to estimate the interest rate process. The results show that the effect of mean reversion is not statistically significant and that volatility is highly sensitive to the level of interest rates. The results prove also that both the drift and the diffusion functions should be nonlinear and that the nonlinear specification proposed by Ait Sahalia (1996b) model is not accurate.