Title: A Bayesian quantile time series model for asset returns
Authors: Jim Griffin - University of Kent (United Kingdom)
Gelly Mitrodima - LSE (United Kingdom) [presenting]
Abstract: The conditional distribution of asset returns has been widely studied in the literature using a wide range of methods that usually model its conditional variance. However, empirical studies show that other features of the distribution may also vary over time. In particular, the returns of most assets display time-dependence beyond volatility, and there is difficulty with fitting their extreme tails. Our aim is to study the time variation in the shape of the return distribution described by a collection of conditional quantiles. Direct modelling of quantile for Bayesian inference is challenging, since it involves analytic expressions for both the quantile function and its inverse to define the likelihood. Thus, we propose a novel class of Bayesian nonparametric priors for quantiles built around a random transformation. This allows fast and efficient Markov chain Monte Carlo (MCMC) methods to be applied for posterior simulation and forecasting. Under this Bayesian nonparametric framework, we avoid strong parametric assumptions about the underlying distribution, and so we obtain a model that is flexible about the shape of the distribution. We define a stationary model and we derive the stationary mean and variance of the quantiles. In our empirical exercise, we find that the model fits the data well, offers robust results, and acceptable forecasts for a sample of stock, index, and commodity returns.