Specification testing and semiparametric estimation of regime switching models: An examination of the US short term interest rate

This paper develops a method for quantitatively and qualitatively assessing the adequacy of the normality assumption in regime switching models. A formal test that extends Jarque and Bera’s (1982) normality test to regime switching settings is proposed. Quasi maximum likelihood estimation of regime switching models is shown to be inconsistent. The feasibility of semiparametric identification of regime switching models is shown and a semiparametric estimator is proposed. Empirically, a two regime Gaussian model of the U.S. short term interest rate is shown to be misspecified. The semiparametric estimator reveals one low volatility regime that is well approximated by normality and one high volatility regime that is negatively skewed and leptokurtic relative to the normal distribution.