I done 30 Year Rolling Standard Deviation of Annual Log Returns of US Stock Market Data from Robert Shiller 1871-Present (ie I calculate standard deviation of annual returns from Jan 1871-Jan 1901,Feb 1871-Feb 1901,etc), Rolling Annualized Standard Deviation of Log Returns assuming no autocorrelation (ie I calculate standard deviation of monthly returns from Jan 1871-Jan 1901,Feb 1871-Feb 1901,etc and I multiply the standard deviation with the square root of 12 to annualize it) and Rolling Annualized Standard Deviation of Log Returns assuming autocorrelation (I found out how to scale volatility assuming there is autocorrelation from this video:"https://www.youtube.com/watch?v=_z-08wZUfBc", but please correct me if I am wrong in following his method).
What I found is that even when I am scaling volatiity assuming there is autocorrelation I still cant get annualized volatilty of log returns to match annual volatility of log returns. Could anyone tell me why this is the case?
Here is link to download excel sheet which is containing the calculations behind this chart.
EDIT: Fixed minor mistake with calculations.