Modeling the U.S. Short-Term Interest Rate by Mixture Autoregressive Processes

A new kind of mixture autoregressive model with GARCH errors is introduced and applied to the U.S. short-term interest rate. According to the diagnostic tests developed in the paper and further informal checks the model is capable of capturing volatility persistence and the dependence of volatility on the level of the interest rate. Realizations generated from the estimated model seem stable and their properties resemble those of the observed series closely. The implied drift and diffusion functions are in accordance with the results in much of the literature on continuous-time diffusion models for the short-term interest rate