A new posterior odds analysis is proposed to test for a unit root in volatility
dynamics in the context of stochastic volatility models. Our analysis extends the Bayesian
unit root test of So and Li (1999,Journal of Business Economic Statistics) in the two
important ways. First, a numerically more stable algorithm is introduced to compute
Bayes factor, taking into account the special structure of the competing models. Owing
to its numerical stability, the algorithm overcomes the problem of the diverging “size”
in the marginal likelihood approach. Second, to improve the “power” of the unit root
test, a mixed prior specification with random weights is employed. It is shown that the
posterior odds ratio is the by-product of Bayesian estimation and can be easily computed
by MCMC methods. A simulation study examines the “size” and “power” performances
of the new method. An empirical study, based on time series data covering the subprime
crisis, reveals some interesting results