Is there concrete evidence that statistical arbitrage (historical vs. implied) on higher moments, specifically skewness and kurtosis, can be (significantly) done?
Working from this source, the author finds clear evidence on volatility arbitrage. Which is mainstream, very well understood, and heavily done (e.g. VIX trading). But, to take the discussion further, this research (Chapter 9 - Trading on Deviations of Implied and Historical Distributions) is specifically addressing this question, applied on DAX data, which is not a as liquid as the equivalent US options markets.
Therefore, my main question is: has anyone done any empirical work on this topic and could relate to it?