# How does Cornish-Fisher VaR (aka modified VaR) scale with time?

I have already posted this question in the quant section, maybe the statistics community is more familiar with the topic:

I am thinking about the time-scaling of Cornish-Fisher VaR (see e.g.page 130 here for the formula).

It involves the skewness and the excess-kurtosis of returns. The formula is clear and well studied (and criticized) in various papers for a single time period (e.g. daily returns and a VaR with one-day holding period).

Does anybody know a reference on how to scale it with time? I would be looking for something like the square-root-of-time rule (e.g. daily returns and a VaR with $d$ days holding period). But scaling skewness, kurtosis and volatility separately and plugging them back does not feel good. Any ideas?

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