A Priori Expectations for GARCH-Based VaR Backtests

Summary

The document poses a research question about whether the choice of volatility model can predict Value at Risk backtest outcomes in advance. It asks whether a GARCH-based VaR forecast, for example, should be more likely than an ARCH or unconditional forecast to receive a higher p-value under Kupiec’s proportion-of-failures test or Christoffersen’s Markov test. It also asks whether such expectations could be formally established or discovered with mathematical proofs.

No model, derivation, answer, data, or test results are supplied; the text only frames the question. The distinction matters because a higher p-value is not by itself evidence that a VaR model forecasts risk better: these tests assess specific calibration and independence properties, and their outcomes depend on the data, forecast procedure, and test sample. The document therefore identifies a possible avenue for research rather than providing a conclusion about GARCH or other models.

Key ideas

• The question concerns whether volatility-model choice predicts VaR backtest results.
• Kupiec and Christoffersen tests assess different aspects of VaR forecast performance.
• A higher backtest p-value alone does not establish that a forecast is superior.
• The document proposes theoretical investigation but provides no proof or empirical evidence.

Tags

# Making apriori Statements on VaR Backtests with a Garch Modelled VaR


# Making apriori Statements on VaR Backtests with a Garch Modelled VaR












so I want to find out, if its possible to find out for any backtest for the Value at Risk(Kupics POF or Christophersen's Markov Test), if it is possible to make apriori Statements on Testing results ( p-value; or power or anything ) using different prediction models (GARCH, or unconditional).

I am looking for apriori Statements like: if we'd use the GARCH model to predict the VaR it will be more likely, that the Kupics POF test has a higher p-value then if we'd use the ARCH-model

If Statements like these exists, are the mathematical proof for these Statments? If nothing like this exists, would it be possible to discover similar apriori Statements ( with mathematical proof)?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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