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I'm going to perform a backtest on some VaR estimates (a huge sample) for a personal project. I'm wondering if the tests which are commonly used to evaluate VaR (Christoffersen, Kupiec) are in some way biased when $n\rightarrow +\infty$. In other words, I need the LR ratio of the test to be a finite number but, as in my case, if $n\rightarrow +\infty$ the test seems to give a value of 0, despite the proporption of violations is 'significantly' greater than the $\alpha$ of the VaR estimates. Does anybody have any suggestion? Thanks

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