A Bayesian approach to term structure modeling using heavy‐tailed distributions

In this paper, we introduce a robust extension of the three‐factor model of Diebold and Li ( J. Econometrics , 130: 337–364, 2006) using the class of symmetric scale mixtures of normal distributions. Specific distributions examined include the multivariate normal, Student‐ t , slash, and variance gamma distributions. In the presence of non‐normality in the data, these distributions provide an appealing robust alternative to the routine use of the normal distribution. Using a Bayesian paradigm, we developed an efficient MCMC algorithm for parameter estimation. Moreover, the mixing parameters obtained as a by‐product of the scale mixture representation can be used to identify outliers. Our results reveal that the Diebold–Li models based on the Student‐ t and slash distributions provide significant improvement in in‐sample fit and out‐of‐sample forecast to the US yield data than the usual normal‐based model. Copyright © 2011 John Wiley & Sons, Ltd.