# Backtesting VaR estimates

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