%I American Statistical Association %L discovery10097063 %A JE Griffin %A G Mitrodima %J Journal of Business & Economic Statistics %O This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. %X We consider jointly modeling a finite collection of quantiles over time. Formal Bayesian inference on quantiles is challenging since we need access to both the quantile function and the likelihood. We propose a flexible Bayesian time-varying transformation model, which allows the likelihood and the quantile function to be directly calculated. We derive conditions for stationarity, discuss suitable priors, and describe a Markov chain Monte Carlo algorithm for inference. We illustrate the usefulness of the model for estimation and forecasting on stock, index, and commodity returns. %D 2020 %K Bayesian nonparametrics, Predictive density, Stationarity, Transformation models %T A Bayesian Quantile Time Series Model for Asset Returns