Multiple hypothesis testing of market risk forecasting models

Francesco Paolo Esposito and Mark Cummins

MPRA Paper from University Library of Munich, Germany

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 (search for similar items in EconPapers)
JEL-codes: C12 (search for similar items in EconPapers)
Date: 2015-03-01
New Economics Papers: this item is included in nep-ecm, nep-for and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:64986

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