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Title: Dynamic quantile function models Authors:  Richard Gerlach - University of Sydney (Australia) [presenting]
Wilson Chen - The University of Sydney (Australia)
Gareth Peters - University College London (United Kingdom)
Scott Sisson - University of New South Wales (Austria)
Abstract: A novel way of thinking about the modelling of the time-varying distributions of financial asset returns is presented. Borrowing ideas from symbolic data analysis, data representations beyond scalars and vectors are considered. Specifically, a quantile function is considered as an observation, and a new class of dynamic models for quantile-function-valued (QF-valued) time series is developed. In order to make statistical inferences and account for parameter uncertainty, a method whereby a likelihood function can be constructed for QF-valued data is proposed, and an adaptive MCMC sampling algorithm for simulating from the posterior distribution is developed. Compared to modelling realized measures, modelling the entire quantile function of intra-daily returns allows one to gain more insight into the dynamic structure of price movements. Via simulations, we show that the proposed MCMC algorithm is effective in recovering the posterior distribution. In the empirical study, the new model is applied to analyze one-minute returns for major international stock indices. Through quantile scaling, we further demonstrate the usefulness of our method by forecasting one-step-ahead the Value-at-Risk of daily returns.