I am currently analyzing the Kupiec test used for backtesting $VaR$. Suppose that I backtest a $VaR$ system for $n$ days (for example 250), with a confidence interval of $1-\alpha$ (for example a $1-\alpha =0.99$, thus $\alpha = 0.01$). According to Kupiec test (and using the $VaR$ definition) we know that the probability of having $x$ exceedances is given by a Binomial distribution with parameters $n$ and $\alpha$.
In this formulation, however, the holding period of the VaR does not appear as a parameter. In other words, if I backtest a 1-day $VaR$ or a 5-day $VaR$ with same $n$ and $\alpha$, the probability of the exceedances is always given by the same binomial distribution.
Is there a way to introduce the VaR holding period as a parameter of the Kupiec test?