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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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Is your model Gaussian or Non-gaussian? –  pyCthon Sep 28 '12 at 16:10
    
Actually non-gaussian, but the intricacies there would be probablys significantly higher, so it'd be already nice to have something for the simpler case. I'm looking for perspectives on how to approach the issue, more than specific methods; and one can often devise atleast approximate extensions later anyway. –  Quartz Oct 1 '12 at 9:07
    
why not just use a kupiec test? –  pyCthon Oct 2 '12 at 19:58
    
Also Kupiec tests assume independence. Consider the extreme case of constant backtesting interval=perfect dependence and you get a bernoulli output which does not really allow for much inference. There are fixes, but what I saw was either too crude or too conservative; and after all the Kupiec test is not so good anyway. –  Quartz Oct 17 '12 at 17:33
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