Modeling Short Term Interest Rates by Chih - ying Hsiao and Willi Semmler

The objective of this paper is to model short term interest rate data. Three problems are studied in this paper. First, if we assume that short term interest rates are discrete-time observations of a di usion process, which discretization methods are preferable for parameter estimation and prediction? Second, can we accept the assumption that the short term interest rates are from a discretely observed di usion process? Third, if they are not, how can we improve the modeling of the short term interest rates? We commence by taking the di usion process model suggested by Chan et al (1992) as the data generating process. We employ three discretization methods: the Euler method, the Milstein method and the new local linearization method to obtain discrete-time approximate models. In our numerical experiment three approximate models can be accepted as correctly speci ed and the Euler model, in contrast to some other results in the literature, is not inferior to the other two models. Then we apply these discrete-time approximate models to the short term interest rate data of Germany, the United Kingdom and the U.S. In contrast to the numerical results, all discrete-time models fail to pass the speci cation test. Compared to the numerical results this indicates that the model suggested by Chan et al.(1992) is very unlikely to be the data generating process for the short term interest rate. Therefore, we search for suitable models for the short rate. We do not nd an appropriate model of di usion processes which can reproduce the stylized facts we are concerned with in this paper. Therefore, we turn to a discrete-time framework in this search. We employ an ARMA-ARCH model with level-dependent volatility for the short term interest rates. The new model can provide better level and volatility forecasts. JEL classi cation: C5; E47