We consider jointly modelling 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.

We consider jointly modelling 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.

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