Dynamic Quantile Function Models

TL;DR

This paper introduces a Bayesian dynamic quantile function model for forecasting intra-daily return distributions, using $g$-and-$h$ quantile functions, and demonstrates its effectiveness in predicting Value-at-Risk compared to existing models.

Contribution

The paper develops a novel Bayesian DQF model utilizing $g$-and-$h$ quantile functions for intra-daily return distribution forecasting, with efficient inference and superior VaR prediction performance.

Findings

The DQF model outperforms interval and histogram-based models in VaR forecasting.

QF-valued forecasts enable effective daily VaR prediction via simple quantile regression.

The Bayesian approach provides reliable parameter uncertainty quantification.

Abstract

Motivated by the need for effectively summarising, modelling, and forecasting the distributional characteristics of intra-daily returns, as well as the recent work on forecasting histogram-valued time-series in the area of symbolic data analysis, we develop a time-series model for forecasting quantile-function-valued (QF-valued) daily summaries for intra-daily returns. We call this model the dynamic quantile function (DQF) model. Instead of a histogram, we propose to use a $g$-and-$h$ quantile function to summarise the distribution of intra-daily returns. We work with a Bayesian formulation of the DQF model in order to make statistical inference while accounting for parameter uncertainty; an efficient MCMC algorithm is developed for sampling-based posterior inference. Using ten international market indices and approximately 2,000 days of out-of-sample data from each market, the performance of the DQF model compares favourably, in terms of forecasting VaR of intra-daily returns, against the interval-valued and histogram-valued time-series models. Additionally, we demonstrate that the QF-valued forecasts can be used to forecast VaR measures at the daily timescale via a simple quantile regression model on daily returns (QR-DQF). In certain markets, the resulting QR-DQF model is able to provide competitive VaR forecasts for daily returns.