Dependence Challenges in VaR Backtesting with Overlapping Horizons

Summary

The document raises the dependence problem that arises when value-at-risk backtests use overlapping time intervals. Overlapping observations share returns, so exceedance indicators or regression residuals may not be independent. This complicates independence tests and can make standard backtesting conclusions unreliable unless the dependence is removed or modeled.

It notes that regression methods have been studied in this setting, while the available work on VaR backtesting is described as limited and unconvincing. The text does not present a specific test, adjustment, or evidence, and it cautions against simply using nearby horizons for reasons it leaves unstated. It is therefore a research question highlighting an inference challenge rather than a proposed solution.

Key ideas

• Overlapping time intervals create dependence between observations used in VaR backtests.
• Dependence can undermine independence tests applied to VaR exceedances.
• Regression approaches exist in related settings, but the document describes VaR-specific work as limited.
• The text identifies a methodological concern without prescribing or validating a correction.

Tags

# VaR backtesting with overlapping time intervals


# VaR backtesting with overlapping time intervals












Of course the issue here is dependence: can it be removed or accounted for (in independence tests too, which of course would be troublesome)? There's a lot of literature on regression in this setting, but little (and unconvincing) on VaR backtesting... We don't want to use near horizons for various (mostly obvious) reasons.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.