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My understanding of VaR model back testing is thus:

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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.

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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!)

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  • $\begingroup$ The VaR backtest may seem unintuitive looking backwards, but looking forward you would indeed on each day take the recent data to forecast VaR. $\endgroup$ – emcor Jan 19 '15 at 22:25
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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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  • $\begingroup$ On the one hand I agree - models that put more weight on new data adapt better. On the other hand though, statistical testing is usually based on IID sampling, which is probably not the case here - hence the question... $\endgroup$ – user3264325 Nov 21 '14 at 0:41
  • $\begingroup$ You are right, but that would require an unrealistic amount of historical data. Moreover, the further we go into the past history becomes less relevant. In practical terms, using overlapping historical data is probably the best way to backtest a VaR producing model. $\endgroup$ – jaamor Nov 21 '14 at 14:59
  • $\begingroup$ '[T]he further we go into the past history becomes less relevant' well that throws up another good question which we could argue about : ) But, back on topic, I can envisage calculations using smaller non-overlapping look backs which might generate enough of a sample set to be usable for back testing... Ymmv of course... $\endgroup$ – user3264325 Nov 24 '14 at 7:58

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