Modeling the Conditional Mean and Variance of the Short Rate Using Diffusion, GARCH and Moving Average Models

This paper analyzes one potential source of misspecification of existing models of the short-term interest rate and introduces a new class of discrete-time econometric specifications that nests many existing interest rate models as special cases. In existing continuous-time or time-series econometric models, the structural form of conditional means and variances is relatively inflexible in the sense that the existing models do not allow for departures from linearity in the conditional mean and they do not parameterize the diffusion function flexible enough to incorporate serially correlated unexpected news, asymmetry and level effects into the definition of conditional volatility. This study attempts to model the conditional distribution of interest rates by specifying a more general econometric framework, which allows for nonlinear effects in the dynamics of the short rate and defines the conditional volatility as a nonlinear function of unexpected information shocks and interest rate levels. The empirical results point to the presence of nonlinearity in the conditional mean, and serial correlation, asymmetry and level effects in the conditional variance of the short rate. In addition, the relative performance of the new class of models in predicting the future level and variance of interest rate changes is found to be superior to the moving-average, diffusion, and GARCH models