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Title: A Bayesian dynamic quantile model for forecasting asset return distributions Authors:  Jim Griffin - University of Kent (United Kingdom)
Gelly Mitrodima - LSE (United Kingdom) [presenting]
Abstract: An approximation likelihood function is proposed for a set of quantiles for Bayesian methodology, which addresses estimation issues that arise in dynamic quantile regression. Our approximation is based on an idea from survival analysis, where the hazard rate functions represent the local scale parameters since they are the scale of the distribution in different intervals. More specifically, we jointly model the distance between quantiles via an observation-driven time series model to approximate the density of asset returns. The underlying idea of the model is that the parameters are updated by using the score function of the likelihood and so the parameters are moving in the direction of the maximum likelihood estimator (MLE) at each time point. Thus, the shape of the conditional density of the observation is associated with the dynamics of the parameters. We consider a zero median distribution function, where the distance from the median becomes the sum of autoregressive processes and generates much more persistence as we move further out in the tails. In addition, the proposed model assumes that the differences of the quantiles evolve linearly over time and therefore we avoid the crossing problem. In our empirical exercise, we find that the model fits the data well, offers robust results and acceptable forecasts for a sample of stock and index returns.