Abstract: In an effort to capture the time variation on the instantaneous return and volatility functions, a family of time-dependent diffusion processes is introduced to model the term structure dynamics. This allows one to examine how the instantaneous return and price volatility change over time and price level. Nonparametric techniques, based on kernel regression, are used to estimate the time-varying coefficient functions in the drift and diffusion. The newly proposed semiparametric model includes most of the well-known short-term interest rate models, such as those proposed by Cox, Ingersoll and Ross (1985) and Chan, Karolyi, Longstaff and Sanders (1992). It can be used to test the goodness-of-fit of these famous time-homogeneous short rate models. The newly proposed method complements the time-homogeneous nonparametric estimation techniques of Stanton (1997) and Fan and Yao (1998), and is shown through simulations to truly capture the heteroscedasticity and time-inhomogeneous structure in volatility. A family of new statistics is introduced to test whether the time-homogeneous models adequately fit interest rates for certain periods of the economy. We illustrate the new methods by using weekly three-month treasury bill data.
Key words and phrases: Diffusion model, kernel regression, nonparametric goodness-of-fit.