Dynamic quantile function models. Issue 9 (2nd September 2022)

• Record Type: Journal Article
• Authors: Chen, Wilson Ye; Peters, Gareth W.; Gerlach, Richard H.; Sisson, Scott A.
• Is Part Of: Quantitative finance. Volume 22:Issue 9(2022)
• Page Start: 1665
• Page End: 1691
• Publication Date: 2022-09-02
• Subjects: Markov chain Monte Carlo -- g-and-h distributions -- Quantile functions -- Symbolic data -- Value-at-Risk; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2022.2053193
• Languages: English
• ISSNs: 1469-7688

Abstract

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 2000 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.