  Stochastic volatility processes are used in multivariate time-series analysis
to track time-varying patterns in covariance matrices. Uhlig extended and
beta-Bartlett processes are especially convenient for analyzing
high-dimensional time-series because they are conjugate with Wishart
likelihoods. In this article, we show that Uhlig extended and beta-Bartlett are
closely related, but not equivalent: their hyperparameters can be matched so
that they have the same forward-filtered posteriors and one-step ahead
forecasts, but different joint (smoothed) posterior distributions. Under this
circumstance, Bayes factors can't discriminate the models and alternative
approaches to model comparison are needed. We illustrate these issues in a
retrospective analysis of volatilities of returns of foreign exchange rates.
Additionally, we provide a backward sampling algorithm for the beta-Bartlett
process, for which retrospective analysis had not been developed.
