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Title: Dynamic quantile function modelling Authors:  Richard Gerlach - University of Sydney (Australia) [presenting]
Abstract: Modelling the time-varying distributions of financial returns has been an interest to many authors in recent decades. The increasing availability of high-frequency data has presented new challenges, namely, effectively making use of the noisy information contained in the intra-daily observations at a reasonable computational cost. Borrowing ideas from symbolic data analysis (SDA), we consider data representations beyond scalars and vectors. Specifically, we consider a quantile function as an observation, and propose a class of dynamic models for quantile-function-valued time series. Direct modelling of quantile functions can be more convenient in applications where the quantity of interest is a quantile. We present a method whereby a likelihood function can be defined for quantile function-valued data, and develop an MCMC algorithm for simulating from the posterior distribution. In the empirical study, we model the time series of quantile functions of high frequency financial returns, and demostrate the usefulness of our method by forecasting one-step-ahead the extreme quantiles of intra-daily returns. Furthermore, through a simple empirical scaling rule, we are able to forecast one-step-ahead the Value-at-Risk of daily returns.