Dynamic quantile function models

Motivated by the need for effectively summarising, modelling, and forecasting distributional characteristics of intra-daily returns, as well recent work on histogram-valued time-series in area symbolic data analysis, we develop a model quantile-function-valued (QF-valued) daily summaries returns. We call this dynamic quantile function (DQF) model. Instead histogram, propose to use g-and-h summarise distribution with Bayesian formulation DQF order make statistical inference while accounting parameter uncertainty; an efficient MCMC algorithm is developed sampling-based posterior inference. Using ten international market indices approximately 2000 days out-of-sample from each market, performance compares favourably, terms VaR against interval-valued models. Additionally, demonstrate that QF-valued forecasts can be used forecast measures at timescale via simple regression returns (QR-DQF). In certain markets, resulting QR-DQF able provide competitive