Has anyone tried using realized range (RR), Martens, van Dijk (2005), as an alternative to range-based measures of vol such as Avg True Range (ATR)?  I'm looking for a scale-invariant range-based measure of vol and ATR doesn't meet that hurdle.  


Here's a link to the paper:
http://www.econ.ku.dk/fru/Conference/Programme/Friday/A6/Martens.pdf  

The RR equation is given on p.4 of the paper and is very easy to test run in Excel.  

I ran a quick regression of RR vs. ATR on the Euro FX and Swiss FX contracts for 1 year of daily data each and came up with an Rsq > 0.979 for both contracts.  So, my quick read is that RR is capturing the range-based characteristics of ATR fairly closely.

My problem with interpreting the paper is what exactly is the mean, std dev, and higher moments?  My impression is that the std dev is RR^(1/2).  I'm not sure how they're calculating the mean.  If anyone can tell me what the 1st and 2nd moments are for the RR I'd really appreciate it.