Dynamic Quantile Function Models

37 Pages Posted: 17 Jul 2017

See all articles by Wilson Chen

Wilson Chen

University of Sydney Business School

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Richard H. Gerlach

University of Sydney

Scott Sisson

University of New South Wales (UNSW) - School of Mathematics and Statistics

Date Written: July 9, 2017

Abstract

We offer a novel way of thinking about the modelling of the time-varying distributions of financial asset returns. Borrowing ideas from symbolic data analysis, we consider data representations beyond scalars and vectors. Specifically, we consider a quantile function as an observation, and develop a new class of dynamic models for quantile-function-valued (QF-valued) time series. In order to make statistical inferences and account for parameter uncertainty, we propose a method whereby a likelihood function can be constructed for QF-valued data, and develop an adaptive MCMC sampling algorithm for simulating from the posterior distribution. Compared to modelling realised measures, modelling the entire quantile functions 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, and that the posterior means are reasonable point estimates of the model parameters. For empirical studies, the new model is applied to analysing one-minute returns of 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.

Keywords: symbolic data, time series, MCMC, quantile function, g-and-h, Value-at-Risk

Suggested Citation

Chen, Wilson and Peters, Gareth and Gerlach, Richard H. and Sisson, Scott, Dynamic Quantile Function Models (July 9, 2017). Available at SSRN: https://ssrn.com/abstract=2999451 or http://dx.doi.org/10.2139/ssrn.2999451

Wilson Chen

University of Sydney Business School

Cnr. of Codrington and Rose Streets
Sydney, NSW 2006
Australia

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Richard H. Gerlach

University of Sydney ( email )

Room 483, Building H04
University of Sydney
Sydney, NSW 2006
Australia
+ 612 9351 3944 (Phone)
+ 612 9351 6409 (Fax)

HOME PAGE: http://www.econ.usyd.edu.au/staff/richardg

Scott Sisson

University of New South Wales (UNSW) - School of Mathematics and Statistics ( email )

Sydney, 2052
Australia

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