Multiple Hypothesis Testing of Market Risk Forecasting Models

25 Pages Posted: 11 Jun 2015

See all articles by Francesco Esposito

Francesco Esposito

Dublin City University Business School

Mark Cummins

Dublin City University Business School

Date Written: June 11, 2015

Abstract

Extending previous risk model backtesting literature, we construct multiple hypothesis testing (MHT) with the stationary bootstrap. We conduct multiple tests which control for the generalized confidence level and employ the bootstrap MHT to design multiple comparison testing. We consider absolute and relative predictive ability to test a range of competing risk models, focusing on Value-at-Risk (VaR) and Expected Shortfall (ExS). In devising the test for the absolute predictive ability, we take the route of recent literature and construct balanced simultaneous confidence sets that control for the generalized family-wise error rate, which is the joint probability of rejecting true hypotheses. We implement a step-down method which increases the power of the MHT in isolating false discoveries. In testing for the ExS model predictive ability, we design a new simple test to draw inference about recursive model forecasting capability. In the second suite of statistical testing, we develop a novel device for measuring the relative predictive ability in the bootstrap MHT framework. The device, we coin multiple comparison mapping, provides a statistically robust instrument designed to answer the question: ''which model is the best model?''.

Keywords: value-at-risk, expected shortfall, bootstrap multiple hypothesis testing, generalized familywise error rate, multiple comparison map

JEL Classification: c12

Suggested Citation

Esposito, Francesco and Cummins, Mark, Multiple Hypothesis Testing of Market Risk Forecasting Models (June 11, 2015). Available at SSRN: https://ssrn.com/abstract=2617146 or http://dx.doi.org/10.2139/ssrn.2617146

Francesco Esposito (Contact Author)

Dublin City University Business School ( email )

Dublin 9
Ireland

Mark Cummins

Dublin City University Business School ( email )

Dublin 9
Ireland

Register to save articles to
your library

Register

Paper statistics

Downloads
55
Abstract Views
434
rank
375,666
PlumX Metrics