Regime-switching univariate diffusion models of the short-term interest rate

Abstract

This article proposes a general regime-switching univariate diffusion model and estimates it using short-term interest rates. The maximum likelihood estimates are obtained using the weekly series of U.S. three-month treasury bill rates. The estimation results reveal that there are strong evidences for the existence of high and low volatility regimes, for the time varying transition probability of the regime variable, and for the high persistence of both regimes. The volatility, but not the drift, is estimated accurately and plays a key role in explaining the dynamics of the interest rates. High persistences and different volatilities of two regimes can well explain volatility clustering observed in the data. Based on the inferred probability of the process being in each regime, most of the high volatility periods correspond to some historic events. The likelihood-based test implies that misspecification can result in misleading outcomes particularly regarding the volatility and transition probabilities of the regime index.