what does "mean of log percentage of trading volume of index"? if we have a pool of volume index, how do we calculate the above? Thanks for the help
Log is logarithm.
"Mean" is what most non-mathematicians call "average".
So, assuming they mean exactly what they said: Gather values of the index you want to analyze. Convert the values to percentages (of what isn't clear). Take the logarithm of each of those percentages. Add those all up and divide the sum by the number of values you used.
In my opinion, the resulting statistic will not help you predict future behavior of the market. But obviously there are people who disagree with me. You should probably ask one of those people for a more specific description of how to calculate this and why they think you should care about it.