How to annualize kurtosis of returns (in simple terms)?

I'm confused by this post on how to annualize kurtosis. I don't understand how to apply it to annualize the kurtosis for my data. In other words, if I evaluated the kurtosis of, say, monthly returns (computed by $$r_{t+1}=\frac{Price(t+1)}{Price(t)}-1$$), what is the number I should multiply it by to get the annualized kurtosis?

• Does this help? quant.stackexchange.com/q/3667/848 Aug 8 '21 at 13:17
• Hello Bob! Yes, I also read your post, but again I didn't find an affirmative answer for the linear returns. The answer there is given for log returns. And this confuses me. Aug 8 '21 at 13:26
• Hi; assuming that 1) the returns are independent across time 2) returns are sufficiently small, you could approximate the moments and moment scaling behaviour of $z_{t,N}\equiv\prod_{i=1}^N(1+r_{t-i+1})-1$ with the same properties as under log returns. In any case, you could verify your assumptions / results using simulation studies. Aug 9 '21 at 9:41