Overlapping Historical Windows in VaR Backtesting

Summary

The document asks whether rolling VaR estimates create dependence in a backtest because adjacent estimates use nearly the same historical observations. Its setup calculates VaR from the preceding n days, then compares the next day’s return with that estimate and records any breach. The concern is that this overlap may reduce the independence of the breach sample and affect conditional or unconditional backtests.

The answer argues that overlap is appropriate when evaluating a model as it would have operated through time: each estimate should use the information available at that date, and a new observation can change the estimate. It therefore sees no inherent problem with overlapping lookback windows. The response is brief and does not derive test properties, compare alternative sampling schemes, or discuss how overlapping estimates affect particular backtest statistics. Its conclusion is best read as a modeling rationale, not a detailed statistical demonstration.

Key ideas

• Rolling VaR backtests compare each day’s realized return with a VaR estimate built from information available before that day.
• Adjacent rolling estimates share most of their historical observations, which motivates concern about dependence in breach data.
• The answer treats this overlap as part of testing how a model would adapt as new data arrive.
• The response does not quantify the effect of overlap on specific backtest procedures.

Tags

# Overlapping Value-at-Risk Backtest Data an Issue?


# Overlapping Value-at-Risk Backtest Data an Issue?












My understanding of VaR model back testing is thus:

~~

t: Calculate daily VaR using look back data over n past days

t+1: Compare daily return against VaR, record breach if one occurred, repeat

Apply conditional and unconditional tests to back test the VaR model.

~~

My question is the danger of VaR look back periods overlapping.

In the above case adjacent VaRs use n-1 days of the same data; much reducing the independence of our back test sample.

I have read a few papers on VaR and none point to this issue - is it just me or is there nothing to worry about here?

Perhaps the conditional tests control for this somewhat, as they should spot clustering of breaches - but surely this would be less of an issue if the data used in the back tests are mutually exclusive.

(I have read previous questions posted and none directly asked this question, thought it was worth a shot!)

## Answer by jaamor (score 2)

https://quant.stackexchange.com/a/15554

When you backtest VaR, you are essentially backtesting your model. You are essentially saying: "If I had this model back in 2007, what would be its calculated VaR?"

The model is tested given all available information up to that time. A good model will adapt given new data and the VaR will change after an extreme event. Even one data point should make a difference.

Therefore, I do not see a problem with using overlapping historical periods.

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