Journal of Time Series Analysis

Extending the Limits of Backtesting via the ‘Vanishing p’‐Approach

Early View

We derive backtests of value‐at‐risk and expected shortfall forecasts for levels that vanish as a function of the sample size n. In the standard case, the level of the forecasts is assumed to be fixed, leading to χ 2‐limiting distributions of the Portmanteau‐type backtests. We show that for levels vanishing at the order of n −1/2, Poisson‐type limits arise instead. These mimic key features of the test statistics, such as discreteness. Simulations demonstrate that for forecast levels and sample sizes of practical interest, using the Poisson‐type limits leads to much improved size vis‐à‐vis the standard χ 2‐limits.

Related Topics

Related Publications

Related Content

Site Footer

Address:

This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on StatisticsViews.com are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and StatisticsViews.com express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.